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MENTAL TESTS 



MENTAL TESTS 



BY 

PHILIP BOSWOOD BALLARD 

M.A., D.Lit. 

AUTHOR OF " OBLIVISCENCE AND REMINISCENCE," AND "HANDWORK 
AS AN EDUCATIONAL MEDIUM " 



HODDER AND STOUGHTON, LTD. 

LONDON NEW YORK TORONTO 
1920 






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PREFACE 

The aim of this little book (its achievement is 
another matter) is to make the teacher his own 
critic, and the teacher's critic a just and discriminat- 
ing judge. By the teacher's critic I mean the 
head master, the inspector or the examiner — whoever, 
in fact, passes an authoritative judgment on his 
work. The teacher and his judge do not always 
see eye to eye ; and the judge, holding as he does 
the position of authority, is prone to press his point 
of view. If he cannot convince he commands. 
And, indeed, if he is to justify his post what else 
can he do ? A difference of opinion about the 
temperature of the classroom may be composed 
by an appeal to the thermometer ; a difference of 
opinion about the average height of the pupils may 
be settled by resort to the foot-rule. But in the 
realm of mind there are, it is thought, no thermo- 
meters and foot-rules : and we sorely need them. 
We need objective measurements recognised by 
all as final and unassailable. Indeed, we shall have 
benefited but little from the new psychology if we 
are not, critic and teacher alike, made aware of our 
own complexes — our whims and grooves and fads — 

v 



vi PREFACE 

our prejudices masquerading as principles, and our 
personal standards laying claim to universality. 
Even if we cannot identify these complexes, to 
know that they are there is something : it makes us 
rigorous in judging ourselves, cautious in judging 
others, grateful for a means of escape from the 
precariousness of individual judgment. To provide 
a few such avenues of escape is one of the purposes 
of the book. 

A common malady among teachers, especially 
women teachers, is over-anxiety about their work. 
They worry about the progress of their pupils, and 
are peculiarly sensitive to the opinion of those in 
authority. And those who worry the most are often 
those who have the least cause for worry. The best 
cure for this infirmity is knowledge ; knowledge of 
the pupils, their aptitudes and attainments ; know- 
ledge of the best means of measuring progress and 
assessing results ; knowledge of what can be done 
by other children, and other teachers. And it is 
hoped that a little wholesome medicine of this kind 
will be found in these pages. 

The solution offered depends ultimately on 
measurement. There are some who instinctively 
dislike the idea of bringing measurement into educa- 
tion. They urge that the highest products of 
education, being spiritual, are outside the realm of 
time and space to which measurements properly 
belong. A partial reply to this argument will be 
found in Chapter I. Here I will merely observe 



PREFACE vii 

that it is possible to extend the notion of measure- 
ment beyond the physical realm ; and that the 
fact that some of the products of education cannot 
be measured is no reason why we should measure 
none. We do, in fact, measure, either well or ill, 
whenever we examine. If we examine at all we 
should examine well ; and to examine well is to 
measure accurately. 

No claim of novelty is made for the way in which 
the subject is treated. Much space is devoted to 
putting before the reader the attempts made in 
England and abroad to arrive at a scientific system 
of testing. The author's own modest contributions 
to the science are to be found mainly in the chapters 
on Reading and Arithmetic. 

In a slightly different form some of the chapters 
have already appeared in the Times Educational 
Supplement and in the Journal of Experimental 
Pedagogy ; and for permission to reprint them I 
am indebted to the courtesy and kindness of the two 
editors concerned. The chapter on the Develop- 
ment of Mental Tests was read before the Educa- 
tional Section of the British Psychological Society, 
and the chapter on Practical Ability before the 
Educational Handwork Association. 

My personal obligations are many. To the 
teachers who have so ungrudgingly helped me to 
standardise the tests ; to Professor T. Percy Nunn for 
his valuable criticism of the chapter on Distribution 
and Dispersion ; to Dr. Emrys Jones for correcting 



viti PREFACE 

the proofs — to all these I am deeply grateful. But 
of all my debts of gratitude by far the biggest is due 
to my friend Mr. Cyril Burt, who has not only let 
me use his revision of Binet's Tests, and include his 
tests of Reasoning and of Spelling, but has carefully 
read through the whole of the manuscript and given 
me the benefit of abundant criticisms and sugges- 
tions. And all this did he do spontaneously : he 
volunteered his help when he heard that I was 
writing on Mental Tests — an act of generosity made 
all the more striking by the fact that he himself 
is about to bring out an important book on the same 
subject. 

P. B. Ballard. 

Chiswick, 1920. 



CONTENTS 



CHAP. 

PREFACE . 

I. THE DEVELOPMENT OF MENTAL TESTS 
II. INTELLIGENCE AND KNOWLEDGE 

III. THE MEASUREMENT OF INTELLIGENCE 

IV. BINET'S TESTS OF INTELLIGENCE 
V. BURT'S REASONING TESTS 

VI. THE MEASUREMENT OF KNOWLEDGE . 

VII. DISTRIBUTION AND DISPERSION 

VIII. READING — 

(a) AS A MECHANICAL ART . 

(/;) AS A MEANS OF ACQUIRING IDEAS 

IX. SPELLING ..... 

X. ARITHMETIC — 

(a) THE FUNDAMENTAL PROCESSES 
{b) SIMPLE ORAL ARITHMETIC 
(f) ARITHMETICAL DEVICES 
(d) APPLIED ARITHMETIC . 

XI. PRACTICAL ABILITY 

XII. COMPOSITION 

APPENDIX. SOCRATES ON INTELLIGENCE 

INDEX ...... 



PAGE 

V 

I 

22 
29 
48 
90 
I06 
115 

134 
145 

155 

l6o 
186 
I90 
191 

196 

2IO 

221 

233 



IX 



MENTAL TESTS 
CHAPTER I 

THE DEVELOPMENT OF MENTAL TESTS 

It is a truism to say that advance in any branch 
of physical science is largely dependent on improve- 
ment in its mathematics. As the science develops 
it gets more and more precise. It begins by being 
qualitative only : it ends by being quantitative as 
well. Indeed, no generalising idea, however illumin- 
ating it may seem, can establish its validity and 
become recognised as a law of nature, unless it can 
be proved by the exact measurement of the facts 
it is designed to unify and explain. Jevons, in his 
Principles of Science, points out that Newton held 
back his theory of Gravitation for fifteen years 
because he found that it did not fit the accepted 
facts about the orbit of the moon. When it was 
possible to measure the orbit more exactly it was 
found that the revised figures, instead of refuting 
his theory, confirmed it to the full. Wisely or 
foolishly he rejected the undulatory theory of light 
in favour of the corpuscular because he had no 
means of measuring with sufficient precision the 
way in which, and the extent to which, a ray of 
light is bent out of its course by the edge of an 

B 



MENTAL TESTS 



opaque body. A still more striking instance of the 
importance of precise measurement is afforded by 
the recent achievements of Einstein. Everybody, 
indeed, admits the importance of measurement in 
physical things, but when it comes to mental things 
people become sceptical. They admit that measur- 
ing would be admirable if it could be done ; but it 
cannot be done. We can measure sticks and stones, 
but we cannot measure ideas. We can fathom the 
depth of a well, but we cannot fathom the depth of 
an emotion. That is the opinion of the frank 
opponents of mental measurements. The other 
side is concisely put by Thorndike : " Everything that 
exists exists in some amount, and if it exists in some 
amount it can be measured." Here we have the 
creed of the mental tester : the belief that in some 
way or other, at some time or other, the most 
subtle mental processes and the" most elusive mental 
products will be made amenable to measurement. 
It is not the test itself that is so difficult : it is the 
evaluating of the product, giving to the result a 
definite position in a graduated scale, assigning to it, 
in fact, a number, a mark or a score ; and so 
assigning it that it has objective value. It must 
not be a guess, but a genuine measurement arrived 
at by means of a technique which would in every- 
body's hands yield, within assignable limits of error, 
the same score. 

Mental tests are as old as the human race. A 
man never consciously and deliberately learns any- 
thing without testing himself ; he never effectively 
teaches anything without testing his pupils. All 
competitive examinations and all school examina- 
tions are series of mental tests. And we know that 



DEVELOPMENT OF MENTAL TESTS 3 

competitive examinations began in China nearly 
4000 years ago, and that school examinations are 
as old as schools. Then there are the mental tests 
that figure so largely in legend and story, the 
riddles that baffle the learning of the learned and 
are solved by the wisdom of the simple. (Edipus and 
the Sphinx, Samson and the lion, are types of stories 
where the test is of mental prowess as distinct from 
bodily prowess. But these were mere pass-or-fail 
tests : they were not designed to graduate, but 
merely to select or sift. 

The earliest attempts at real mental measurements 
were of the nature of indirect measurements. Just 
as we cannot measure electricity directly, but by 
measuring something else whose size varies con- 
comitantly with the strength of the electric current 
can get a result which serves our purpose just as 
well, so it was thought that some kind of vicarious 
measurement might be found for the mind. And 
the most plausible concomitant was the head. 
This was the idea of Gall, the father of Phrenology. 
At the close of the eighteenth century he and his 
disciple, Spurzheim, taught that the head was an 
index of the brain, and the brain an index of the 
mind. They did not go so far as to say that a big 
head meant a big mind, but they did assert that the 
relative proportions of the skull and the configura- 
tion of its surface, would, when exactly measured, 
yield an exact indication of the mental powers. 
The palmy days of phrenology were the early 
decades of the nineteenth century. Nearly every- 
body then believed in bumps. My readers will 
recall an account of a certain dinner-party where 
an unaccustomed guest solemnly asked the company 



MENTAL TESTS 



whether they did not think Milton a great poet ; 
and Charles Lamb, who was present, said he wanted 
to feel the gentleman's bumps. Indeed, most of 
us can remember the day when the cultured house- 
hold was prone to lay great store by a china head 
mapped out in plots. But we no longer display 
these things in the home, nor use them in the study. 
Phrenology has, in fact, failed to establish its claims. 
If it is science at all it differs from all other sciences 
by standing still. The charts that we see to-day 
in O'Dell's window in Ludgate Circus are to all 
intents and purposes the charts used by Gall and 
Spurzheim a hundred years ago. 

Older even than phrenology is physiognomy. 
Nearly thirty years before Gall expounded his 
theory of the skull Lavater put forward his theory 
of the face. In the year 1772, when Gall was a 
boy of fourteen, Lavater published his celebrated 
essay on Physiognomy. His doctrine was that the 
face, not the cranium, was the index of the mind. 
A man's fighting qualities, for instance, resided in 
his nose. A nose that protruded near the root like 
a Roman nose meant an aggressive disposition. It 
was the nose of attack. If it protruded in the 
middle it meant a propensity to fight for others. 
If it protruded at the point it meant an aptitude 
for self-defence. The retrousse nose was neither 
inquisitive nor self-assertive, but merely self- 
defensive. 

Shrewd as some of Lavater's observations were, he 
made the fundamental mistake of confusing the 
bony structure of the face with its fleshy covering. 
He regarded the contours of the cheek-bone as 
much an expression of character as the lines round 



DEVELOPMENT OF MENTAL TESTS 5 

the mouth. Many years later, after the science 
had emerged somewhat from the eclipse into which 
it had been thrown by phrenology, the study of the 
face was taken up afresh by scientists like Bell and 
Darwin. They, however, definitely discarded the 
osteology of the face in favour of its sarcology, and 
devoted their attention to the mobile and plastic 
covering, the changes in which seemed to betoken 
the prevailing modes of thought and feeling. 
Physiognomy became, in fact, the science of expres- 
sion, and only indirectly and suggestively the science 
of character and intellect. If a man, for instance, 
has crow's-feet round his eyes before he is forty, 
it seems no very wild conjecture to assume that he 
smiles much and is of an amiable disposition. But 
as weak eyes, as well as a kind heart, may cause 
crow's-feet, the inference becomes somewhat pre- 
carious. Indeed, Darwin never pretended that 
physiognomy was an exact science. We cannot 
measure a smile or a sneer or a look of surprise. 
Heine states in his Florentine Nights that he 
does not know whether the mouths of Parisian 
women are large or small, because one can never 
tell where the mouth leaves off and the smile 
begins. 

The next attempt to physiologise the mind was 
Lombroso's. He was a criminologist who tried to 
find the bodily peculiarities that went with con- 
firmed evil-doing. He searched for certain marks 
or malformations which he called stigmata, and 
which he thought would distinguish the criminal 
type. A lack of symmetry, for instance, in form 
or feature was supposed to be one of the common 
signs of degeneration. We admit its commonness, 



MENTAL TESTS 



for we are all in some degree branded with it. 
This line of research, however, has fallen into 
discredit. It is now-a-days believed that if there 
is a criminal type we must seek its characteristics 
in the mind and its behaviour, rather than in the 
body and its anatomy. 

The man who gave the greatest impetus to mental 
measurement in England was Sir Francis Galton. 
But he was primarily an anthropologist, with a 
bias towards physical measurements and com- 
parative anatomy. He was imbued with a belief 
that some sort of correspondence could be found 
between intelligence and certain bodily traits, such 
as the length of the middle finger, the character of 
the finger-prints, and the span of the open arms as 
compared with stature. And researches in this 
direction have not proved altogether fruitless. If 
they did nothing else they gave us the Bertillon 
system of identification by finger-prints. But they 
did not bring us appreciably nearer the object of 
our quest. The physical correlate of intelligence 
was still undiscovered. It was left to Professor 
Karl Pearson to deliver the most crushing blow to 
the belief that we can find a physical scale for 
mental facts. In 1906 he published the result of 
an elaborate investigation into the relationship 
between intelligence and the size and shape of the 
skull. And his verdict was that the connection 
between them, if it existed at all, was so slight as 
to be of no use for purposes of inference. Here 
ends the first phase of the search for a scale to 
measure mind. The conclusion reached was definite 
enough, but entirely negative. We cannot tell 
a criminal by looking at him ; we cannot tell a genius 



DEVELOPMENT OF MENTAL TESTS 7 

by the shape of his skull ; and we cannot tell a fool 
by the length of his ears. 

But this does not dispose of physical measurements. 
For it was next argued that although we cannot 
measure the mind by measuring the body, we may 
be able/ to do so by measuring the powers of the 
body. /A static measurement failed, but a dynamic 
measurement might succeed. For as soon as the 
body does something, unless that something is 
purely automatic, the mind co-operates in the work. 
Volition, at least, is brought into play. This view 
led to experiments with the various instruments 
for measuring muscular strength and skill. The 
dynamometer, for instance, measures the strength 
of one's grip, and the ergograph the strength and 
endurance of the middle finger. But valuable as 
these instruments were for testing fatigue, they 
revealed no sort of relationship between mental and 
muscular traits. The tapping test was more promis- 
ing. In its simplest form it consists in seeing how 
many taps per second the subject can make with a 
pencil on paper. It is found that one can tap 
faster with the right hand than with the left, and 
it is a conceivable hypothesis that a very stupid 
person is, if I may use an Irishism, left-handed all 
over his body. But although tapping afforded some 
indication of motor ability it did not signify the 
presence of any form of intellectual ability. 

Reaction-time experiments ran on the same line. 
It was found that people differed considerably in 
the rapidity with which they responded to a 
stimulus ; and a delicate apparatus was devised to 
measure the time that elapsed between the hearing 
of a sound and the pressing of a button ; or between 



8 MENTAL TESTS 

some other signal and some other motor response. 
This test is an excellent vocational test. Rapid 
reaction is important to the boxer, whose aim is to 
get his fist in first, and to the airman who needs, 
at the sight of danger, to press the right lever at the 
right time in response to the right signal. 

It will be observed that the quest begins to lose 
its singleness of purpose. The measurements began 
by being physical, then they became psycho physical, 
ultimately they became almost purely psychical. 
As soon as the psychical element came in at all, 
any measurement that was achieved was to a certain 
extent a psychical measurement. But to measure 
a particular mental function for its own sake is one 
thing : to measure it in the hope of finding it an 
index of general mental ability is quite another thing. 
The latter has always been the bigger problem ; 
but the former is by no means devoid of purpose and 
value. To be able to measure any mental function 
whatever, however limited its operation, is no mean 
achievement, and in the types of experiments to 
be now recounted definite measurements have been 
attained which have proved valuable in develop- 
ing psychological theory, and serviceable in their 
application to various pursuits in life. It is only 
in the larger quest that they have comparatively 
failed. 

In the nineteenth century attempts were made to 
measure sensations. Weber put forward his cele- 
brated law, which was afterwards interpreted and 
elaborated by Fechner. It was supposed to establish 
a relationship between the physical stimulus and the 
sensation it produced, or, rather, between the way 
in which an increase in the intensity of the stimulus 



DEVELOPMENT OF MENTAL TESTS 9 

was accompanied by an increase in the intensity 
of the sensation. In the sixties and seventies of 
last century the Weber-Fechner law gave rise to 
numerous discussions. While some thought that it 
revealed the connecting-link between mind and 
body and was of immense metaphysical import, 
others held that it was merely an instance of the 
general law of relativity : it merely illustrated the 
fact that we judge things not absolutely but 
relatively. But although the Weber-Fechner law 
is regarded as of little importance now-a-days — of 
little importance to the educationist at least — the 
researches to which it led have considerably advanced 
the science of mental measurements. Means were 
devised, for instance, for measuring the acuity of 
the various forms of sense-perception, particularly 
of seeing and hearing. More important still, it led 
to the measurement of sensory discrimination — of 
the fineness with which we can detect differences 
in things. For it was suspected that here lurked 
the clue for which the intelligence-hunters were 
searching. Indeed, the comparison of lines and the 
comparison of weights are widely used to-day as 
tests of intelligence. It was sensory discrimination 
in the skin, however, that gave rise to the most 
sanguine hopes. Early in this century an eminent 
psychologist expressed the belief that he had found 
a trustworthy instrument for measuring general 
intelligence. That instrument was the Eesthesio- 
meter. The sesthesiometer consists of a pair of 
sharp points, like the points of a pair of compasses, 
one of which can be shifted back and fore on a 
graduated scale. When the points are applied to the 
skin of a blindfolded subject they are felt as one 



io MENTAL TESTS 

point unless they stand a certain distance apart. 
The least distance apart at which they are felt as 
two points is the discrimination threshold. It was 
believed that the sensitivity of the skin, as indicated 
by this threshold, was a key to the acuteness of the 
mind ; that if a man was thick-skinned he was 
thick-headed as well. But when the supporters of 
this theory tried to prove it they found they 
could not do so. It was found that if sensory dis- 
crimination of the skin was an index of anything at 
all, it was just as likely to be of stupidity as of 
intelligence ; for McDougall and Rivers were able 
to show that the savages on the shores of the Torres 
Straits had more discriminative skins than Europeans. 
So the sesthesiometer was, after all, merely an 
sesthesiometer and not a phrenometer : it measured 
sensitivity, but not sensibleness. 

The scientific study of memory began with 
Ebbinghaus, who was the first to measure memory 
in its simplest form — in the form of retaining and 
reproducing nonsense syllables — sounds devoid of 
all sense and all associations. He laid the foundation 
of modern laboratory methods of testing memory, 
and of the distinction made in all pedagogical tests 
between rote memory and substance memory. 
Galton devised rough-and-ready means of estimating 
the vividness of visual imagery. Later psychologists 
have used ink-blots for measuring the rapidity with 
which images emerge in the mind. A series of blots 
are shown the subject, and a record made of the 
time he takes to name the object suggested by 
each. 

It were both tedious and superfluous to take the 
reader through the various means that have been 



DEVELOPMENT OF MENTAL TESTS n 

invented for measuring the different mental faculties 
— processes which, in fact, are neither simple nor 
separate — processes such as attention, perception, 
apperception, memory, imagination and reasoning. 
And whenever an instrument or piece of apparatus 
is used for any of these purposes it is always impossible 
to claim that it singles out and tests one simple 
and unitary mental function. One of the most 
useful pieces of apparatus, for instance, in the 
psychological laboratory is McDougall's dotting 
machine. A strip of paper marked with an irregular 
zig-zag row of small circles passes at a rate regulated 
by clock-work behind a slot which enables only a 
small number of circles to be exposed at a time. 
The subject has to mark with a pencil the centre 
of each circle as it passes before him. This machine 
is used to test fatigue, to test attention and to test 
accuracy of aim ; and there may be other kinds of 
ability that it tests as well. 

In the meantime, while specific tests were being 
rapidly devised and improved, what progress took 
place in the measurement of general intelligence ? 
This can be best illustrated by reference to the 
experiments of Mr. Cyril Burt, who has done more 
to solve this particular problem than any other 
British psychologist. Mr. Burt began his investiga- 
tions among school-children in Oxford about the 
time that Binet published his first series of tests in 
1905. His method was to select the group of 
children in a school who fell within certain age 
limits (say from twelve and a half to thirteen and a 
half years old), and to get the head teacher and class 
teachers to arrange these children in order of intel- 
ligence, relying partly on their empirical judgment, 



12 MENTAL TESTS 

and partly on the results of the school examina- 
tions. Then the children were given individually 
twelve psychological tests, ranging from simple 
sensory and motor tests to tests of voluntary atten- 
tion, and it was calculated to what extent the 
results tallied with the teachers' empirical estimate. 
The higher the correlation between the two orders, 
the more satisfactory was the test regarded as an 
index of intelligence. Some five years later Mr. Burt 
made a further investigation at Liverpool, using 
tests of a higher and more complex kind — extending 
them, in fact, so as to include various types of 
reasoning. He was thus able to range in a sort of 
hierarchy, on the basis of their value as criteria of 
intelligence, a large series of tests involving mental 
processes of widely varying levels. And the con- 
clusion he arrived at was that when we have arranged 
them in the order of their complexity we have already 
roughly arranged them in their order as intelligence- 
measurers. And of all the tests of intelligence those 
that measure the power of thinking, that is, the 
power to understand and to reason, are the best. 
Thus is common sense vindicated by the psychologist- 
Thus we have arrived at the conviction that if we 
wish to test intelligence we must test it directly 
and not indirectly : we must test those very mental 
processes which the plain man regards as intelligent. 
We must note whether the subject is " quick in the 
uptake," whether he has " nous " or " gumption," 
whether he can " see beyond his nose." And it 
will be observed, too, that instruments and machines 
have been relegated to the psychological laboratory, 
where they are of inestimable value both to pure 
psychology and to certain branches of applied 



DEVELOPMENT OF MENTAL TESTS 13 

psychology. For educational purposes they are of 
little use. At any rate, it is certain that no machine 
has yet been invented which will measure intelli- 
gence ; and faith in the possibility of such a machine 
is growing fainter every day. We now regard 
laboratory tests and school tests as distinct things — 
a position which was taken up from the very first 
by that pioneer of educational experiments, Mr. 
Winch. 

At this stage we have abandoned certain specious 
by-paths which seemed to lead to the desired goal, 
and we have found the true path, which has, after 
all, proved to be the common high road which the 
mass of humanity has been treading all along. But 
in one sense we are as far from the goal as ever. We 
know the kind of test to be applied, but we have no 
scale. We can test, but we cannot measure. It 
was left for Binet to discover the scale. And the 
full significance of his discovery is rarely realised. 
His critics — and they are very numerous — have bee a 
so concerned in pointing out what he has not done 
that they have neglected to give him credit for what 
he has done. And Binet's crowning glory is, not 
that he got together a medley of heterogeneous tests 
for the detection of the feeble-minded, but that he 
invented a scale. In this he resembles Saul, the 
Son of Kish, who set out to look for asses and found 
a kingdom. Binet's scale is his kingdom ; not the 
individual tests — these may so change that there is 
nothing recognisable left — but the scale itself. 
Its principle is age-performance. He took a certain 
test, such as, say, counting backwards from twenty to 
nought, applied it to a large number of children, 
found the lowest age at which between 60 and 70 per 



1 4 MENTAL TESTS 

cent, of the children passed, and allocated the test 
to that age. Thus he has a series of about five 
tests for each age ; and if a child of five passes the 
tests for seven, his mental age is recorded as two years 
in advance of his chronological age. Thus the unit 
of his scale was one year of mental age. It was a 
plan so simple and obvious that one wonders that it 
never was used before. But it is certain that it 
never was. We came near it in the old Standards 
of Examination that were issued by the Board of 
Education in the days of payment by results. But 
they just missed it through being an arbitrary scale, 
based on opinion and not on actual age-performance. 
And in modern standardised tests the standard is 
always actually, or ideally, an age-performance. 

Binet regarded intelligence as a complex process 
whose main characteristics were threefold : its 
purposefulness, its capacity for making adaptation, 
and its power of self-criticism. He therefore made 
his tests as heterogeneous as possible. He looked 
everywhere for tests, and showed much sagacity in 
finding those that were simple, practical and effective. 
They involve such ordinary questions as : " Are you 
a little boy or a little girl ? " and such unusual 
problems as : Put the following words in such order 
that they make sense — 

To Asked Spelling 
My I Master 
Correct My. 

And he used no apparatus. The only material 
required, beyond what is found in an ordinary school- 
room, is a series of five pill-boxes similar in size 
and appearance, but differently loaded. 



DEVELOPMENT OF MENTAL TESTS 15 

Binet's scheme led to abundant controversy. 
Indeed, the literature of the controversy would fill a 
small library. Everybody abused Binet, and every- 
body used him. They said his tests were very bad, 
but they were the best we had. If Binet had lived 
he would have improved his tests, for he was con- 
tinually revising them. He, indeed, issued three 
series— the 1905, the 1908 and the 191 1 series — each 
an improvement on the previous one ; and just 
before he died in 191 3 he was engaged in making ^' 
another revision. His line of research was en- 
thusiastically taken up in America, where three 
important revisions were issued, the Goddard 
revision, the Yerkes point-scale revision (where the 
method of marking was changed), and finally the 
revision that should be best known in this country, 
the Stanford revision, carried out by Terman. The 
basis in each case was Binet, and the alterations 
and extensions were matter of detail rather than of 
principle. The tests applied to the recruits for 
the American Army were partly based on Binet ; 
the tests used for Matriculants at Columbia Uni- 
versity were inspired by Binet's, and the tests used 
in Berlin to select supernormal children are imitative 
of Binet's. The only extension of principle is the 
addition of group-tests. Binet's tests are indi- 
vidual, and it takes from half-an-hour to an hour 
to examine a single subject. A large number of 
new tests have been devised, which may be applied 
simultaneously to a large number of pupils ; but 
they agree with Binet's in being age-performance 
tests, and in being tests of intelligence rather than 
of acquired knowledge. 

The latest development of the Binet system is 



1 6 MENTAL TESTS 

to be found in Burt's system of Reasoning Tests ; 
or rather, it is the logical outcome of Burt's own 
theories, for the only part of Binet's system that he 
retains is the age-performance basis of selection. 
The tests themselves he rejects. If intelligence, 
which Burt defines as " inborn all-round mental 
efficiency " is mainly manifested in the higher 
mental processes, the best intelligence tests would 
embody various forms of reasoning, and would omit 
all reference or appeal to the lower mental processes. 
Burt has, accordingly, recently published a series of 
fifty reasoning tests, which are the best of an initial 
list of 250 that were tried on miscellaneous groups 
of children and adults. The questions are not the 
usual syllogistic questions of traditional logic, but 
involve the application of thought to the ordinary 
affairs of life. Where the purpose of the test is to 
pick out the brightest children rather than to pick 
out the blockheads, these tests will, in my opinion, 
prove far more satisfactory than Binet's. They are 
new as yet and have not been extensively used ; 
but I believe there is a great future for them. 
They display much ingenuity, and the more difficult 
tests are far more likely to pick out what Terman 
calls the superior adult than Ter man's own tests. 

So much for intelligence tests. But this is only 
one of the fields in which the technique of mental 
testing has been improved, and in which it has been 
put to practical purposes. Laboratory apparatus 
and laboratory methods have been rapidly improving 
within recent years, and psychological tests have 
been applied with great success in the realms of 
medicine, business and industry. To describe these 
developments here is outside my scope ; I must 



DEVELOPMENT OF MENTAL TESTS 17 

limit myself to mental tests in the educational 
realm, and so far I have not touched the measure- 
ment of school attainments. 

Our success in securing standardised tests and 
standardised measurements depends mainly upon 
three mathematical discoveries. One of these I 
have already dealt with — that of age-performance. 
Before Binet's day we tried to measure one unknown 
by another unknown. We tried to test mental 
processes by means of tests whose difficulty was 
merely a matter of guess-work. We knew neither 
their absolute nor their relative difficulty. Binet 
gave us a method by which the difficulty of the tests 
could be graded and standardised. But he himself 
seems to have made no use of the other two mathe- 
matical conceptions which have largely advanced 
the science of mental measurements — the theory 
of normal distribution, and the theory of correla- 
tion. It was Quetelet, the Belgian mathematician, 
who showed how widely applicable was the law 
of normal distribution, what a large number of 
social and physical phenomena were found to follow 
the normal curve, and how the form of distribution 
could be deduced from the laws of probability. But 
it was Galton who suggested that mental traits 
generally, and intelligence in particular, would be 
found to follow the same law. And to-day this 
curve is universally used to test tests and to certify 
them. If the results do not conform to the normal 
curve they at once become suspect. Goddard and 
Terman have amply demonstrated that Binet's 
tests triumphantly stand this criterion of validity. 
To Galton, too, we are mainly indebted for the 
doctrine of correlation, which has proved so valuable 
c 



1 8 MENTAL TESTS 

an instrument in determining the extent to which 
two orders of measurements tally with each other — 
or, in other words, the extent to which two functions 
vary concomitantly. The doctrine of Correlation 
was developed and elaborated by Professor Karl 
Pearson, to whom we owe the formula most com- 
monly used. Professor Spearman discovered a 
formula of correlation which, although not so 
strictly accurate as Karl Pearson's, is much simpler 
to use, and is quite satisfactory when the rank only 
of the subjects is known. This correlation formula 
was extensively used by Burt, and has figured 
largely in the exposition and proof of the doctrine 
of Intelligence as conceived by Spearman and his 
school. 

Another device which has proved of great service 
is that of " equal grasps," invented by Mr. Winch. 
Each child in one group is paired with another 
child of equal merit in the other group. Such an 
arrangement enables the experimenter to estimate 
the efficacy of a new method of teaching, or to 
compare the efficacy of two rival methods ; for one 
group may be taught by one method and the 
other group by the other method. 

It remains for me to deal with the development 
of mental tests in the realm of school studies — a 
realm where mental tests in the form of examina- 
tions have from time immemorial been regarded 
as an essential part of the school machinery. But 
the newer system of school tests differs essentially 
from examinations. An examination, however care- 
fully it is conducted, is a test of comparative ability. 
It enables the examiner to arrange his examinees 
in order of proficiency. But it does not enable 



DEVELOPMENT OF MENTAL TESTS 19 

him to compare the proficiency of the group as a 
whole with the proficiency of any other group as 
a whole, nor yet with the normal achievement of 
other pupils under similar conditions of age and 
schooling. For a public examination is like a 
rocket : it can be used but once. It measures, it 
is true ; but it measures the individuals of a group 
one against the other : it does not measure them by 
reference to a standard scale. The newer tests, 
on the other hand, are standardised tests : they are 
tests whose difficulty is already known in terms of 
age-achievement. The separate tests, of which an 
examination consists, are either regarded as carrying 
equal marks, or as carrying marks which vary in 
accordance with the examiner's opinion of their 
difficulty or their importance. Standardised tests, 
on the other hand, do not depend for the marks 
they carry on anybody's mere opinion, but rather 
on their difficulty as experimentally determined. 
The tests are tested and standardised by a mathe- 
matical analysis of the results obtained by applying 
the tests to a large number of children. The sub- 
jective element is reduced to a minimum, and the 
objective element raised to a maximum. 

The extent to which objective tests of school 
studies are possible depends partly on the study 
itself, and partly on what aspect of the study it is 
desired to test. Proficiency in arithmetic, for 
instance, is easier to test objectively than pro- 
ficiency in English composition ; and proficiency in 
the fundamental processes of arithmetic easier than 
proficiency in the capacity to apply these processes. 
This difference in the degrees of objectivity is still 
more readily seen in the attempts that have been 



2 o MENTAL TESTS 

made to measure the various aspects of reading. 
For proficiency in reading depends upon at least 
three distinct types of ability — ability to translate 
symbols into sounds, ability to absorb meaning, 
and ability to read aloud so as to make the meaning 
intelligible to others. These are concerned with 
the mechanical aspect, the intellectual aspect and 
the elocutionary aspect respectively. The first 
ability is easy to measure, the second difficult, the 
third almost impossible. Apart from a few abortive 
experiments with the dictaphone nobody has ever 
attempted to invent standardised tests of elocu- 
tionary power. 

In America alone have educational tests received 
the attention they deserve. There a number of 
tests have been devised and norms established in 
arithmetic, reading, spelling, grammar, geometry 
and algebra. All these rest on the same basic 
principle as Binet's Intelligence tests, except that 
grade-performance is substituted for age-perform- 
ance. The standardised tests in composition, and 
handwriting and drawing, however, involve an 
entirely new principle — a principle which, though 
not invented by Professor Thorndike, is mainly 
associated with his name. It consists in devising 
a scale of typical specimens, a scale arrived at by 
collating the opinions of a number of independent 
judges. When it is wished to mark a particular 
paper, it is compared with the specimens of the 
standard scale with a view to discovering to which it 
is most nearly equal in merit. If the variability in 
the marking of the same set of papers by a number 
of independent teachers is less when the scale is 
used than when it is not used, it is claimed that 



DEVELOPMENT OF MENTAL TESTS 21 

the use of the scale is justified. As a matter of fact 
it is found that after some practice in the use of 
the scale the variability is less ; but not so much 
less as to give this type of measurement any very 
high degree of objective validity. Even in America 
the scales are not used much. In England they are 
not used at all. But the other scales are to a certain 
extent. We have not, in this country, gone far in 
the invention of tests and the establishments of 
norms ; but we have begun the work, and we are 
slowly but steadily forging ahead. 



CHAPTER II 

INTELLIGENCE AND KNOWLEDGE 

All who have given serious thought to education 
have been wont to exalt intelligence at the expense 
of knowledge. " Wisdom," says an ancient writer, 
" is the principal thing ; therefore get wisdom ; 
and with all thy getting get understanding." And 
although by wisdom he doubtless meant something 
more than intelligence, he at least meant intelligence. 
On the other hand, " he that increaseth knowledge 
increaseth sorrow." Here in these far-off times we 
see recognised a distinction which has much exer- 
cised the mind of the modern educationist — the 
distinction between wisdom and learning, intelli- 
gence and knowledge, mental power and mental 
content. 

The cry for intelligence was acutely clamant 
in the first decade of the twentieth century. The 
primary schools had just recovered from the cramp- 
ing effect of annual examinations and had begun to 
breathe more freely. Intelligence became a cult 
and a quest and a watchword. Teachers aimed at it ; 
inspectors looked for it ; administrators encour- 
aged it. There was a " slump " in accuracy and 
a " boom " in intelligence. And the educational 
psychologist, seeing herein a promising field for his 
labours, began to investigate intelligence and to 



INTELLIGENCE AND KNOWLEDGE 23 

cast about for means to measure it. Although 
Binet's name was alone prominent before the public, 
he was by no means the only investigator ; nor, 
perhaps, the most original. Still, the work he 
achieved was great. He had a genius for discerning 
what was worthy in the work of others ; he cast his 
net so wide that nothing valuable escaped him ; 
and — most important point of all — he kept a steady 
eye on practicability. 

But while the teacher tried to cultivate intelli- 
gence, and the psychologist tried to measure in- 
telligence, nobody seemed to know precisely what 
intelligence was. It was certain that the term 
covered a wide field. When at a recent meeting 
of an education committee a member asserted that 
teachers as a body were highly trained and intelli- 
gent, an opponent (advocatus diaboli) retorted that 
the same was true of elephants. Clearly there was 
need to sharpen and define the term. It is not 
enough to say that it means ability as distinct from 
knowledge, capacity as distinct from content, power 
as distinct from product. For how can we gauge a 
mind's capacity except by finding out what it can 
contain ? But what it contains is knowledge. And 
how can we measure a mind's power without 
measuring its product ? But its product is, again, 
in part at least, knowledge. Binet saw this diffi- 
culty, and frankly accepted knowledge as one of the 
many marks of intelligence. One of his earlier 
intelligence tests, for instance, for a child of nine 
is : name in order the days of the week. He would 
probably argue that a child of nine who in his inter- 
course with his fellow-creatures had not picked up 
these names was necessarily somewhat stupid, 



24 MENTAL TESTS 

Binet was inclined to adopt the easy-going attitude 
of the artist, who does not mind a notion being 
nebulous so long as it is workable, rather than that 
of the scientist, who strives for precision and con- 
sistency at all costs. 

There are other psychologists, however, who 
have taken up the question in a different spirit ; 
most notably Professor Spearman in England and 
Professor Thorndike in America. Their mode of 
research was mathematical. They submitted specific 
mental abilities — the ability to add numbers, to 
memorise words, to discriminate lengths, to sort 
cards, and so forth — to certain rigid tests, and care- 
fully marked the results. Then they compared the 
various scorings and found the correlation between 
them ; that is, the degree of concomitant variation, 
or the extent to which the compared abilities tend 
to rise and fall together. And from similar statistics 
the two investigators arrived at entirely different 
conclusions. Thorndike concluded that the indi- 
vidual abilities were entirely independent ; that 
there was, in fact, no such thing as general intelli- 
gence, but only particular intelligences. For may 
not a man be intelligent at geometry and stupid 
at history, or brilliant as a poet and hopelessly bad 
at figures ? Spearman, on the other hand, con- 
cluded that there was a certain dominant factor 
common to all the specific abilities, a central fund 
of intellective energy, to which the term general 
intelligence or general ability might fitly be applied. 
To put it in another way, Thorndike held that a 
man's intellectual wealth consisted entirely of 
coupons ; Spearman that it consisted partly of 
coupons, each of which may be expended in one 



INTELLIGENCE AND KNOWLEDGE 25 

direction only, and partly of cash, which could 
be expended in any direction. Both views recog- 
nised the obvious fact that individuals varied widely 
in intellectual wealth ; the views clashed on the 
question of the availability of that wealth. 

Let us examine the ground of the belief in 
general intelligence. It is a matter of common 
observation that a man who is good at one thing is 
good at most other things. At least it is so as a rule ; 
cases of one-sided ability are very rare. Generally 
speaking, a wise man is wise in all things, a fool is 
a fool all round. Indeed, it can be proved mathe- 
matically that there is a positive correlation between 
all forms of native ability ; they always tend to 
hang together ; the odds are always in favour of 
high ability in any given function being accom- 
panied by high ability in any other function. Why 
should this be ? Why should mathematical ability 
be positively correlated, as it is, with linguistic 
ability ? Even if we make every allowance for 
such operations as might be conceived to be common 
to the two abilities, we still fail to account for the 
whole relationship. There still remains an un- 
explained nexus. We are forced, in fact, to assume 
a general factor common to all the multifarious 
operations of the mind, a factor with which each 
specific ability is, in its own measure, charged and 
energised. This common factor is intelligence. 
Such is Spearman's reasoning ; and its cogency is 
hard to dispute. But he further arrives at the dis- 
concerting conclusion that this central factor cannot 
be cultivated. It is born with one, and can neither 
be improved by schooling nor dulled by neglect. 
Intelligence is mother wit, and mother wit is a 



26 MENTAL TESTS 

matter of heredity. The ancient writer already 
quoted holds a more hopeful view. He believes in 
the possibility of cultivating wisdom. But even he 
admits that it is sometimes difficult : " Though thou 
shouldest bray a fool in a mortar among wheat, 
with a pestle, yet will not his foolishness depart 
from him." 

It follows from this that the only practical thing 
a psychologist can do with general intelligence, if 
there is such a thing, is to measure it. Hence the 
assiduous pursuit of mental tests. It is clear that 
general intelligence cannot be directly tested, for 
it can never be found alone : it is always embedded, 
as it were, in specific abilities. But can it not be 
tested indirectly ? We have in the thermometer 
an excellent example of indirect measurement. 
There are no known means of measuring temperature 
directly ; we have to make use of the fact that the 
expansion of a thin column of mercury is almost 
perfectly correlated with temperature. So instead 
of measuring the temperature, we measure the 
mercury ; which does quite as well. Now is there 
not some simple function of mind or body which 
when measured will give us in the same way an exact 
valuation of intelligence ? The quest of this key- 
ability resembled the quest of the philosopher's 
stone. It sometimes led to the discovery of un- 
expected treasure ; it often led to the discovery of 
mare's nests ; it always, as far as the essential search 
was concerned, ended in disappointment. Every 
device failed that assumed an essential corre- 
spondence of soul with sense and sought to measure 
mind through matter. 

There was no help for it. The hope of finding 



INTELLIGENCE AND KNOWLEDGE 27 

a simple key-ability had to be abandoned ; and 
investigators had to fall back on the laborious 
expedient of testing as many abilities as possible and, 
by a process of mathematical analysis, extracting 
the common intellective element. Among the 
pioneers in this particular field of research, Mr. 
Cyril Burt takes the foremost place. After years 
of patient labour he proved that while almost any 
kind of ability was a presumptive sign of intelligence, 
some abilities were much safer signs than others. 
To use his own words : " Of all the tests proposed, 
those involving higher mental processes, such as 
reasoning, vary most closely with intelligence." 

There are no tests of intelligence that are more 
widely used than Binet's. And Binet's tests are 
based on the principles I have just expounded. 
Like Spearman and Burt, he discarded brass instru- 
ments, and relied more on the higher mental pro- 
cesses than on the lower/ His tests measure general 
ability simply because they measure a large number 
of specific abilities. So far as he is concerned, it 
does not in the least matter whether Spearman is 
right or Thorndike ; on either theory his tests are 
a real, though rough, measure of individual mental 
endowment. 

William James, in advocating his pragmatic 
method, contends that the best way to discover the 
essential difference between two conflicting theories 
is to find out the practical difference in the conse- 
quences that flow from them. How, in fact, do 
they affect practice ? We have seen that, whichever 
of the rival theories of Spearman and Thorndike 
be accepted, it makes no difference in the mode of 
testing ; does it make any difference to the teacher ? 



28 MENTAL TESTS 

Again the answer is " No." On either view the 
only cultivable thing is the multifarious group of 
special abilities. It must not, however, be thought 
that all this theorising and researching has had no 
effect on school practice. It most distinctly has. 
Its effect has been to broaden the outlook, to 
multiply the school pursuits, to vary and amplify 
the methods of study. 



CHAPTER III 

THE MEASUREMENT OF INTELLIGENCE 

The British Press refers to mental tests as though 
they were new things invented by Americans. In 
point of fact they are neither new nor American. 
They have been the common property of the race 
since the dawn of history. They are no more 
mysterious than the conundrums that delight 
children at a Christmas party. They are, in fact, 
merely questions or tasks that invite a trial of 
intelligence. What is new is not the tests them- 
selves, but the aptness with which they are chosen 
and the scientific precision with which they are 
applied. 

A tacit distinction seems to be made between 
examinations and mental tests. This distinction 
is illegitimate ; for an examination is nothing but 
a series of tests, which are just as mental or psycho- 
logical as any that have ever been devised. They 
are not non-mental tests, but simply a special kind 
of mental test. The real distinction lies between 
tests of knowledge and tests of ability ; tests of 
school attainments and tests of natural intelligence ; 
tests of book-learning and tests of mother-wit — a 
distinction which is easy to make but difficult to 
maintain. For it is impossible to devise a test of 
ability which does not also test knowledge, and 

29 



30 MENTAL TESTS 

impossible to devise a test of knowledge which does 
not also test ability. Let us, for example, take one 
of the most characteristic of Binet's intelligence 
tests. The child is asked to say what is absurd in 
the following : " If I should ever grow desperate 
and kill myself, I will not choose Friday, because 
Friday is an unlucky day and will bring me unhappi- 
ness." To answer this correctly he must know, 
among other things, the meanings of the words, 
and he must know that a dead man is, in this world 
at least, neither happy nor unhappy. If the ques- 
tion were put in these words to a unilingual China- 
man he could never answer it, however intelligent 
he might be ; and to a race of immortals it would 
be meaningless. Now let us consider this peda- 
gogical test : Which are the four largest towns in 
Scotland ? A correct answer would at least involve 
ability to grasp a fact and to remember it, to under- 
stand a question and to respond to it. The differ- 
ence between the two types is one of proportion. 
To answer the second we must acquire a special bit 
of knowledge which casual experience will not 
necessarily force upon us ; to answer the first 
involves the application of such knowledge as no 
sane mortal can fail to pick up in the ordinary 
course of life. 

The distinction, however, so far as it goes, is 
perfectly sound, and indeed is constantly cropping 
up in the folk-lore and legends of all races. The 
point of the old English ballad of King John and the 
Abbot depends entirely on this distinction. The 
king sets the abbot three mental tests. At the 
risk of forfeiting his life in case of failure, the abbot 
has to say what the king is worth, how long it 



MEASUREMENT OF INTELLIGENCE 31 

would take him to ride round the world, and what 
he is thinking of. A respite of three weeks is given. 
The abbot cudgels his poor brains in vain. He rides 
to " Cambridge and Oxenford, but never a doctor 
there was so wise that could with his learning an 
answer devise." In fact, the only man who could 
rescue him from his plight was his own shepherd, 
a man who could neither read nor write. The 
shepherd, who happened to resemble his master in 
appearance, disguised himself as the abbot, pre- 
sented himself before the king, and spoke thus : 
" How much are you worth ? Twenty-nine pieces 
of silver, for you are worth at least one piece less 
than our Saviour. How long will it take you to 
ride round the world ? You must rise with the 
sun, and ride with the sun, until he rises here again 
next day ; then the journey will take you" exactly 
twenty-four hours. What do you think ? You 
think I'm the abbot ; but I'm not : I'm his shep- 
herd." Here we have three tests, which all the 
learning in the land could not satisfy, triumphantly 
solved by simple mother-wit. And, indeed, all 
through the records of folk-lore and mythology do 
we find the learning of the learned put to confusion 
by the wisdom of the simple. The supreme ordeal 
which reveals the native nobility of the hero is just 
as likely to be the solution of an enigma or the 
interpretation of a dream as the slaying of a dragon 
or a giant. While the dragon is the test of physical 
prowess, the enigma is the test of intellectual 
prowess. Perseus by his courage rescued Andro- 
meda, but (Edipus by his intelligence rescued the 
whole of Thebes. As the reader will remember, 
the riddle of the Sphinx (" What animal walks in 



32 MENTAL TESTS 

the morning on four legs, at noon on two, and in 
the evening on three ? ") was solved by OEdipus 
alone, a king's son reared by peasants, a man in whom 
nature triumphed over nurture. 

The whole family of riddles, puzzles, charades 
and conundrums belongs to a larger group of ability 
tests. They require for their solution no special 
knowledge, but a general aptitude for applying 
knowledge — for the discernment of subtle analogies 
and contrasts. We must not, however, fall into 
the error of thinking that the modern application 
of mental tests consists in the mere asking of riddles. 
The tests are, in a sense, riddles, but they are riddles 
of a special kind : they must have diagnostic value. 
Let me illustrate by comparing an old riddle with a 
new test. The riddle is : What relation does a 
loaf of bread bear to a steam-engine ? And the 
test : Complete the analogy : As a loaf of bread 

is to a glass of water, so is eating to . The 

answer to the riddle is " mother " ; for a loaf of 
bread is a necessity, a steam-engine an invention, 
and necessity is the mother of invention. This is 
not a test of intelligence, but of a perverted ingenuity. 
It is not intended to gauge one's reasoning powers, 
but to raise a laugh. As a means of diagnosis it is 
quite useless, unless, indeed, one gives the result a 
negative interpretation ; for success in its solution 
is, as a mark of sanity, no more significant than 
failure. It is sophistry rather than logic, a jest 
rather than a test. Very different is the analogies 
test given above. Failure to answer this would, in 
an adult, mean a serious defect of intellect. For 
its solution lies not in some crooked by-path of 
sophistry, but on the great highway of human 



MEASUREMENT OF INTELLIGENCE 33 

thought. That is why it serves for a diagnosis of 
mental endowment and unfoldment. For there is 
a certain stage of mental development below which 
it cannot be answered, and above which it cannot 
be mis-answered. Although, therefore, the enigmas 
of the ancients and the catch-questions of to-day 
are, in the broad sense of the term, mental tests, 
they lack the special characteristics of those tests 
which are now-a-days called mental or psychological. 
The whole point and pungency of the riddle or the 
catch lies in its being exceptional. To repeat it in 
another form is to thwart its purpose. For its 
purpose is to trip us up ; and once the trick of it is 
known it ceases to trip us up. After we have got 
the hang of such a sentence as " Pas de l'yeux Rhone 
que nous," it is quite easy to read " Guy n'a beau 
dit qui sabot dit nid a beau dit-elle ? " When 
CEdipus, in pondering over the riddle of the Sphinx, 
guessed that " the morning " meant " the morning 
of life," the enigma was virtually solved ; and all 
others based on the same metaphor. The riddle, 
in fact, needs novelty for its success. The nut to 
be cracked may be any nut but a chestnut. 

As distinct from this spurious mental test, the 
genuine mental test depends for its value upon its 
universality. It is always a member of a family, 
and the larger the family the better. The analogies 
test given above may be multiplied indefinitely ; 
indeed, as many as a hundred have been set at one 
sitting. For example : As cat is to kitten, so is 

dog to ? As sheep is to ox, so is flock to ? 

As Paris is to France, so is London to ? In 

testing ability, as in testing knowledge, it is always 
best to set a fair number of questions. To base a 



34 MENTAL TESTS 

judgment on one test, however good that test may 
be, is extremely precarious ; when the test itself 
is suspect, no verdict at all can be reached. Each 
test must itself be tested, and the results inter- 
preted in accordance with the laws of probability. 
I have, for instance, tried the following test on young 
and old : If you are given a corked bottle half full 
of wine, how can you get the wine out without 
taking out the cork or breaking either the cork or 
the bottle ? Most adults proclaim the task im- 
possible, but many a small boy, who has solved 
certain difficulties with his bottle of ginger-beer 
or liquorice water, can answer the question promptly. 
The test, in fact, proves to be too dependent on 
an accident of experience to be a real gauge of 
practical ability. Nor is it necessary to fall back 
on such doubtful tests when we have so many 
that are of demonstrable validity. 

Another element of prime importance in scientific 
testing is speed — an element which is clearly ex- 
emplified in the cancellation test. The subject is 
required to cancel as rapidly as possible all the ah 
or all the rs, or any other letters, separately or 
concurrently, in a page of printed matter. A 
limited time is allowed — say, two minutes. In 
rating the results the marker has to take into account 
the number of letters rightly erased, the number 
wrongly erased, and the omissions. It is obvious 
that with unlimited time all who could distinguish 
the letters at all would score full marks. To ignore 
the time element is to nullify the test. 

If, however, there is one single feature which 
essentially distinguishes the modern test from the 
gncient, it is that the modern test h standardised, 



MEASUREMENT OF INTELLIGENCE 35 

The man who first convinced the world of the 
necessity for standardised tests, as distinct from 
casual and haphazard tests, was Alfred Binet. And 
he achieved it incidentally. What he really was 
after was to find out which children in the schools 
of Paris were mentally defective. To do this he 
devised two carefully graduated scales, one to 
measure school attainments and the other to 
measure general intelligence. The first measured 
roughly, the second more exactly ; the first sifted 
out the suspects, the second found from among the 
suspects the real blockheads. The assumption was 
that all fools are dunces, but all dunces are not 
fools — an assumption quite in accordance with 
common sense. This general scheme, full of flaws 
as it is in detail, has given birth to the whole modern 
system of scientific testing. He has not only shown 
us how to discover intellectual and moral weaklings, 
but he has led us into a fertile land which it is 
our duty to explore and subdue. 

Binet avoided the mistake of trying to deduce a 
scale from first principles. He based his scale on 
fact. Before asserting what degree of intelligence a 
child of ten ought to possess, he took the trouble 
to ascertain what degree of intelligence a child of 
ten actually does possess. Before testing children 
with a test, he first tested the test with children. 
By applying it to a large number of children of 
different ages he was able to fix the lowest age at 
which the majority were able to pass it. Let me 
illustrate this with reference to a type of test which 
was evidently a favourite of Binet's, for in his scale 
of fifty-four intelligence tests it appears four times 
— more frequently, in fact ? than any other. It 



36 MENTAL TESTS 

consists in the repetition of a series of digits. The 
examiner says : " I am going to say x numbers. 
Listen and repeat them after me : 5, 8, 2, . . . 
etc." The numbers are uttered steadilv at intervals 
of half a second. Binet found that at three years 
of age few could repeat three digits, but consider- 
ably more than half could repeat two. Thus he 
fixed the repetition of two digits as a three-year- 
old test ; and acting on the same principle he 
assigned three, five and seven digits to the ages of 
four, eight and fifteen respectively. This innocent 
little test is not, in its implications, so simple as it 
seems. It measures the span of primary memory — 
the number of things one can hold in the conscious 
memory at the same time. It depends on the fact 
that consciousness is not a point but a patch ; and 
the assumption is, the bigger the patch the bigger 
the mind. When the mind ceases to attend to A 
and passes on to B, A does not suddenly vanish from 
consciousness leaving B in sole possession, but 
fades gradually away, forming in the process what 
William James calls a " fringe " to B. If by the 
time the last digit is uttered by the examiner the 
first has quite disappeared from the child's mind, 
the child will fail in the test. His psychic fringe is 
too small. 

The importance of primary memory is more 
apparent in dealing with words than in dealing 
with figures. For if all the essential parts of a 
spoken sentence do not in some sense reverberate 
together in the mind, the sentence has no chance 
of being understood. Fortunately the words in 
connected discourse have greater cohesion than a 
string of digits, and the number of syllables that 



MEASUREMENT OF INTELLIGENCE 37 

can, according to Binet, be repeated at the ages 
of three, five and fifteen amount to six, ten and 
twenty-six respectively. Roughly speaking, a child 
should be able to repeat twice as many syllables as 
the number of years he has lived. Binet's typical 
example for fifteen is : " The other day I saw in 
the street a pretty yellow dog. Little Maurice 
has stained his nice new apron." 

Much interest is attached to Binet's third test 
for children of twelve years of age : " I am going 
to allow you three minutes, and I want you to say 
as many words as you can think of. Some children 
have said more than two hundred ; let me hear 
how many you can say. Ready ? Start." In 
order to pass the child must say at least sixty words. 
This is an ingenious way of finding the child's 
association time — the time it takes one word to call 
up another. The laboratory method is to deal 
separately with each word and to measure precisely 
by means of a specially constructed clock the interval 
that elapses between the hearing of the word and 
the emergence of an associated idea. And, indeed, 
some such plan is necessary in scientific investigations 
of the association process itself. But for measuring 
mental activity in children, for finding roughly 
the rate at which ideas march through the mind, 
Binet's method is equally effective and much 
simpler. Although he uses this test once only, it 
has been found that the number of words a child 
can utter in the given time increases steadily with 
his age ; that norms or averages could consequently 
be fixed, and the test used to mark different levels 
of intelligence. It has also been found that one 
minute will give results just as trustworthy as three 



38 MENTAL TESTS 



minutes. All this serves to illustrate how Binet's 
tests are constantly being criticised and refined 
upon ; how tests themselves are not exempt from 
the testing of time and experience. 

Interesting, however, as these tests are, they are 
probably inferior in diagnostic value to the absurdity 
tests to which I have already referred . And although 
Binet sets them at one point only — ten years of 
age — they are appropriate to all ages except the 
very lowest. The following test, which I devised 
some years ago to arrange rapidly (and of course 
roughly) in order of intelligence a group of children 
of eleven years or over, was found to be suitable for 
all children who could read fluently and were 
advanced enough to express their ideas in writing — 

John Carew lived in a small cottage which stood 
on the top of a barren hill and faced the east. From 
the foot of the hill a grassy plain stretched in every 
direction as far as the eye could see. On the even- 
ing of John's thirtieth birthday, while he was sitting 
on the front door-step looking towards the setting 
sun and watching his shortening shadow on the 
gravel path, he suddenly became aware that a 
horseman was riding down to the cottage. The 
intervening trees and foliage made it difficult for 
him to see clearly, but he was able to perceive 
that the horseman had only one arm. When, 
however, he got a closer view he recognised that the 
visitor was his son William who had left home to 
join the army twenty years before and had not 
been heard of since. On seeing his father William 
immediately dismounted, ran towards him, threw 
his arms round his neck, and burst into tears. 



MEASUREMENT OF INTELLIGENCE 39 

Each child in the class was given this passage in 
print, and was allowed a quarter of an hour to read 
it and to write out any absurdities he could find 
therein. It contains about seven absurdities, and 
it was found that it did actually differentiate the 
children in close accordance with the teacher's 
rating of their general intelligence. Elementary 
school children of eleven years of age who discovered 
at least five absurdities were, as a rule, those who 
on other grounds had been selected as worthy of a 
secondary school training. 

It has been complained that most absurdity tests 
are too easy for the older pupils. Given, however, 
a time limit, it would not be difficult to devise a 
test which would floor the majority of adults. 
Let the reader, for instance, try to find within 
fifteen seconds the absurdity (there is but one) in 
the following : " John Jones, who had married his 
widow's sister, used to say that if a man had a bad 
sister it was his misfortune, but if he had a bad wife 
it was his fault." 

When Binet published his scale in 1908 he regarded 
it as tentative. Indeed, he revised it himself three 
years later ; and since his death many a patient 
experimenter has laboured at separating still further 
the gold from the dross. It has been found that 
while some of the tests are almost worthless, others 
are of no small value : they are reliable in practice 
and suggestive in theory. Moreover, new tests 
are daily being devised and put to the trial of rigid 
experiment, so that we are gradually accumulating 
a body of tests which bear the hall-mark of demon- 
strated success. 

One of the main defects of Binet's scale is its 



4 o MENTAL TESTS 

bias in favour of language — of words rather than 
things ; another defect is the paucity of tests (there 
are but five) prescribed for adults. When therefore 
adults have to be tested for intelligence — and 
especially such illiterate adults as were plentiful in 
the American Army — recourse has to be had to 
tests of a new type. One of the most useful of 
these is the " construction board," a variation of 
the jig-saw puzzle. The sections, however, are 
generally rectangular, and the time always restricted. 

A test which has gained considerable vogue 
during recent years consists merely in the giving of 
instructions to be obeyed by the subject. These 
instructions may possess any degree of complexity 
and may be used to mark the rapidity with which 
the meaning is grasped. For instance : " Print 
your Christian name (or names) in small letters 
and your surname in capitals unless there are more 
than six letters in your surname, in which case you 
should print your surname in small letters and your 
Christian name (or names) in capitals." It is quite 
easy to see how these tests may be indefinitely 
complicated either by making the provisos more 
puzzling or by simply increasing their number. 
As a sample : " If your grandfather's only child was 
your uncle draw a square ; if not, draw a circle." 
Here, as always, a time limit is essential. 

So much for intelligence tests. Binet's other 
scale (his bar erne d' instruction) consisted of ordinary 
examination questions, with the difference — a highly 
important difference — that they have been carefully 
sifted and standardised. The development of this 
scale is quite another story. Nor must the intelli- 
gence tests with which we have been dealing be 



MEASUREMENT OF INTELLIGENCE 41 

confused with vocational tests, which are designed 
to find out what sort of work a person is best fitted 
for. These are just as often physical tests as mental 
tests, and frequently involve the use of delicate and 
complicated apparatus. 

Having made a distinction between the two broad 
types of mental tests (tests of knowledge and tests 
of ability), and having shown that these types are 
never quite pure, let us examine the bearing of this 
theoretical distinction on the practical art of 
examining. There are four possible methods of 
procedure. First, we may dispense with the ordin- 
ary examination altogether and substitute a series 
of ability tests. This is no new proposal. It has 
been made many a time before, but it has always 
been rejected. And rightly so. For it cannot be 
too strongly insisted on that education is directly 
concerned not with natural ability but with culture. 
For natural ability, as scientifically conceived, grows 
with the growth of the brain, fluctuates with fresh- 
ness and fatigue, and varies with varying states of 
health and nutrition. The most that the school- 
master can do is to take full advantage of what 
natural ability his pupils may happen to possess. 
His business is not to train intelligence but to use 
it — to use it himself, and to see that his pupils 
use it. And his success is measured by the degree 
of culture he imparts. But culture means know- 
ledge. True, it means other things as well ; but 
it means knowledge at least. And the most effec- 
tive way of testing knowledge is by examinations. 

The second possibility is to leave things as they 
are — to rely on examinations pure and simple, 
examinations of the good old-fashioned sort. But 



42 MENTAL TESTS 

this policy implies a wilful blindness to certain grave 
defects which have been pointed out repeatedly and 
persistently for the last half -century. 

The third possibility is to hold two distinct 
examinations, one a pedagogical examination, and 
the other a psychological examination — one a test 
of acquired knowledge, the other a test of natural 
aptitude. This is virtually Binet's plan for detect- 
ing the feeble-minded. The teacher sifts first, the 
psychologist afterwards. It is also the scheme that is 
reported to have been recently adopted at Columbia 
University for selecting candidates for entrance. 
Those who pass the ordinary matriculation ex- 
amination are further submitted to a series of tests 
for general intelligence. It is not quite clear 
whether any are knocked out in the second round. 
It is not indeed clear whether the second round 
is intended to knock them out at all. The prob- 
ability is that the second examination is not selective 
but experimental. It is intended to reveal the 
degree of correspondence between the results of 
the two types of examination. Rash indeed would 
be the examiner who would lightly brush aside the 
evidence of combined scholarship and intelligence 
which a wisely conducted examination affords. 
Besides, the virtue of matriculation lies in the fact 
that it guarantees a certain minimum of culture. 
The university starts no course of study from the 
beginning ; it takes up the tale at the point where 
the secondary school left off. It demands of its 
alumni a determinate measure of literacy, and by 
means of a matriculation examination it assures 
itself that its demand is met. And if this demand 
is met — if the candidate has sufficient intelligence 



MEASUREMENT OF INTELLIGENCE 43 

to carry him successfully to that point in the road 
of learning — it would need more proof than our 
modern mental tests can at present afford to demon- 
strate that he can go no farther. If the purpose 
of the second examination is to reduce the element 
of chance, there seems to be more reason for re- 
testing the failures than for re-testing the passes. 
For failures may be due to illness or excessive 
nervousness, or sheer bad luck. Moreover, a high 
degree of intelligence in a candidate may well be 
regarded as counterbalancing certain gaps in his 
store of knowledge. 

The last alternative is to combine both types 
of test in one. examination. When this took place 
in the past- it was mainly a matter of accident; 
now it is done by design. It is the way in which 
the new science of testing has affected English 
examinations. The examiner is beginning to ask 
himself what it is that he is really examining. Is it 
parrot knowledge, or is it knowledge that has been 
intelligently acquired and can be intelligently 
applied ? Is it the application of common know- 
ledge in an unfamiliar field, or is it the application 
of exotic knowledge to familiar instances ? Is it 
the capacity to acquire, or the capacity to express ? 
In any case the wise examiner never neglects to test 
the capacity of the candidate to apply knowledge 
and to express it in new forms, for in so doing he 
kills two birds with one stone : he tests both know- 
ledge and intelligence. Speaking generally, the 
younger the pupil the less the importance to be 
attached to school attainments as distinct from 
native ability. In other words, if intelligence tests 
are important anywhere, they are important at that 



44 MENTAL TESTS 

stage in the pupil's career when we decide upon 
the type of education for which he is best fitted. 
This principle is clearly observed in the selection 
of mentally defective children at the age of seven ; 
less obviously in the selection of supernormal 
children at the age of eleven. It is customary at 
examinations for junior scholarships to set two 
papers only, one in English and the other in arith- 
metic. And the questions are so devised as to 
frustrate, as far as may be, the designs of the 
crammer. That this examination will radically 
change in the near future is highly improbable, 
for it is difficult at present to conceive a better 
practical device for testing annually the intelligence 
of a large number of children. The fact that it is 
conducted every year, or even twice a year, in the 
same schools renders known and standardised tests 
almost useless. If we are to remove entirely the 
possibility of special coaching, the element of 
novelty is essential. And the scope for variety in 
the realm of English and mathematics is virtually 
unbounded. Here intelligent anticipation on the 
part of parents and teachers can readily be defeated. 
Again, the 8000 children who sit every six months 
for the London junior scholarship examination can 
all be examined quite easily in one morning with 
no superintendents besides the ordinary teachers. 
Under the Binet scheme, where the testing is oral 
and individual, it would take a trained examiner 
nearly four years to get through one half-yearly 
batch. To test the whole lot in one morning 
would need the services of 1400 examiners specially 
trained for the purpose. As a matter of fact samples 
of the candidates have been tested by both written 



MEASUREMENT OF INTELLIGENCE 45 

and oral methods, and the results obtained are so 
similar that confidence in the present system is 
amply justified. 

There are two fairly distinct types of ability which 
are tested by these junior examinations — mathe- 
matical ability and literary ability. Proficiency in 
problem arithmetic is in itself no poor criterion. 
One of the most trustworthy of Binet's tests is the 
second in his scale for eight-year-olds : Count 
backwards from twenty to nothing in twenty seconds. 
It is the departure from the beaten track that gives 
it its value. The modern tendency, however, is to 
attach more importance to the English paper than 
to the arithmetic. Binet long ago remarked that 
no child who could compose was mentally defective ; 
and Mr. Cyril Burt, the psychologist to the London 
County Council, has expressed the opinion that the 
school subject most clearly symptomatic of intelli- 
gence is composition, provided it is marked for its 
power of thought. The only serious defect of the 
present system is the absence of tests of the third 
broad type of ability — manual ability. This defect 
has been carefully considered by the London 
authority, who have adopted the view that in 
early years the ablest with their heads are also as 
a general rule the ablest with their hands ; that it 
is very difficult to discover at the age of eleven (that 
is, before the children have begun to attend the 
handicraft and . domestic centres) what practical 
ability children actually do possess ; and, finally, 
that those few children who have a special aptitude 
for craftsmanship and escape the junior county 
scholarship net are captured by the trade scholarships. 

It were unwise to prophesy what developments 



46 MENTAL TESTS 

will take place in English examinations in the near 
future. Already one English authority has included 
in its junior examination a test of the " instruc- 
tions " type given above, and it is not impossible 
that a third paper will become the general rule — a 
paper corresponding to the obsolete general know- 
ledge paper, except that it will aim at discovering 
not whether the candidate is well-informed, but 
whether he is sharp-witted. The secondary schools 
and universities show as yet no alarming symptoms 
of infection. 

Thoughtful people have recently been asking : 
Why is it that America has been moving so rapidly 
in the matter of mental tests while England has 
almost stood still ? The answer is simple : Speaking 
generally, Americans believe in psychology but 
Englishmen do not. When America entered the 
war one of the first things she did was to mobilise 
her psychologists. The war was nearly over before 
England discovered that psychologists were of any 
use. And the discovery was due partly to the 
witnessing of what was achieved in the American 
Army, and partly to an appreciation of the wonder- 
ful results that followed the psychological treat- 
ment of shell-shock and war-strain by those numerous 
psychologists (medical and non-medical) who volun- 
teered their services early in the war. The fault 
did not lie with the British psychologists. In the 
pursuit of their particular science and in the inven- 
tion of new tests they were in no way behind their 
neighbours. And the Americans knew this ; they 
consulted our professors and freely used their tests. 
There is no psychological instrument which is more 
generally useful than the dotting machine, an 



MEASUREMENT OF INTELLIGENCE 47 

invention of Mr. McDougall, of Oxford ; there is 
no instrument more specifically useful than the 
K tube, an invention of Dr. C. S. Myers, of Cam- 
bridge. The new science of testing could never 
have reached its present stage but for the discovery 
of that potent means of mathematical analysis known 
as " correlation." It was discovered by an English- 
man, perfected by an Englishman, and simplified 
for common use by an Englishman. In the investiga- 
tion of general intelligence and in the critical 
examination of the methods used nobody has done 
better work than Mr. Cyril Burt. Like Binet, he 
was concerned in testing tests as well as in testing 
ability. But the methods he adopted were more 
rigidly mathematical. He invented tests too ; among 
others the analogies test mentioned above. Many 
other Englishmen have successfully laboured in the 
same field, such as Mr. W. H. Winch, Dr. W. Brown, 
Dr. E. O. Lewis, Professor J. A. Green, Dr. J. L. 
Mclntyre, Dr. N. Carey, Miss N. Taylor, Mr. 
H. B. English, Miss May Smith, Dr. Bernard Hart, 
and Dr. Edgar Schuster and other investigators in 
the psychological laboratories of University College, 
King's College and Oxford. Such records of their 
work as have already been published may be found 
distributed among the pages of the British Journal 
of Psychology, the Journal of Experimental Pedagogy, 
and the Annual Reports of the British Association. 



CHAPTER IV 

binet's tests of intelligence 

The translation of Binet's Tests given below 
was made by Mr. Cyril Burt in consultation with 
Dr. Simon, who was Binet's collaborator in de- 
vising and standardising the scale. The tests, 
originally standardised for Parisian children, have 
been tried by Mr. Burt on a large number of 
London children, and modified to suit their char- 
acteristic rate of development. The tests, in fact, 
are here rearranged in the order of their freshly 
ascertained difficulty, and the age-assignments are 
given as they were determined afresh for children 
of London Elementary Schools. 

Each child has to be tested individually, and 
under conditions most favourable to the removal 
of shyness and nervousness. The examiner must 
use his discretion respecting the point of the scale 
at which he should begin : the usual rule is to 
start with the group of tests just below the child's 
chronological age. If, however, there is a failure 
in any of those tests it is expedient to go back and 
try all the tests in the previous group. The ex- 
amination should then be carried up the scale until 
the child fails in four or five consecutive tests, 

4 8 



BINET'S TESTS OF INTELLIGENCE 49 

Terman gives as the lowest permissible limit of 
thoroughness a range which starts at the year 
which yields only one failure, and ends with the 
year which yields only one success. To estimate 
the child's mental age the examiner should regard 
the age at which all tests are passed as the base 
age, and should add one-fifth of a year for every 
additional test belonging to any of the higher 
ages ; or, where in the following revision there are 
more or less than five tests in the higher year, the 
corresponding reciprocal fraction. 

It is now customary to state the final result in 
the form of an Intelligence Quotient, a method 
first suggested by the German psychologist, Stern. 
The Intelligence Quotient is found by dividing the 
mental age by the real age. If, for instance, a 
child's real age is eight and his mental age six, 
his intelligence quotient is '75. If his mental 
age were ten his intelligence quotient would be 
1-25. 

Binet lays it down that the amount of retarda- 
tion that determines a child as defective is two 
years when he is under nine, and three years 
when he is past his ninth birthday. Stated in 
terms of the intelligence quotient the border-line 
between normality and deficiency is somewhere 
about '75. No cases, however, where the intelligence 
quotient falls between "j and *8 are quite free from 
doubt. 



50 MENTAL TESTS 



BINET TESTS (BURT'S TRANSLATION 
AND REVISION) 

Age Three 

1. Understanding Simple Commands. 

Instructions. — " Show me (point to, put your 
finger on) — 

(i) your nose. 

(2) your eyes. 

(3) your mouth." 

Evaluation. — All should be correctly performed ; 
but free encouragement may first be given. 

2. Repeating Numbers. 

Instructions. — " I am going to say some numbers. 
Will you listen, and say them after me ? " 

(For use only after failure in first set.) 

5 8 9 

37 64 72 (Age 3) 

714 286 539 (Age 4) 

3681 5749 8526 (Age 5) 

52947 63852 973i8 (Age 6) 

250634 5739 16 495827 (Age 9) 

9647518 4829653 5928136 (Age 11) 

Note : rate should be two per second ; utter- 
ance should be without rhythm, emphasis or in- 
flection. Do not tell the child if he is wrong. 
Do not repeat the same series. Merely give him 



BINET'S TESTS OF INTELLIGENCE 51 

another chance with another series. Failure owing 
to interruption does not count. (While uttering 
the numbers or syllables, hold up the hand or 
finger to prevent the child starting to repeat before 
entire phrase or list has been completed. Drop 
the hand as a signal to child that you have finished 
and he is to repeat.) 

Evaluation. — One correct repetition out of three 
trials counts as success. Note, therefore, the largest 
number the child can repeat. The age at which 
series of different lengths can be repeated is given 
in the last column above. The repetition of figures 
in their natural order, e. g. 9645678, should be noted 
as an instance of automatism. 

3. Naming Own Sex. 

Instructions. — " Are you a little boy or a little 
girl ? " (for a boy). " Are you a little girl or a 
little boy ? " (for a girl). 

If child says " yes " or " no " or merely echoes 
part of the phrase, ask the two questions separ- 
ately : " Are you a little girl ? " " Are you a little 
boy ? " 

4. Giving Surname. 

Instructions. — " What is your name ? " If child 
merely gives Christian name, ask : " And what 
else ? . . . Tommy what ? " 

Evaluation. — If child gives surname he has some- 
times been known by e.g. stepfather, or mother 
(when illegitimate) record it as correct. 



52 MENTAL TESTS 

5. Naming Simple Objects. 

Materials. — A penny, a closed knife, and a 
common kind of key. 

Instructions. — " What is that ? " or " What is 
this called ? " showing each object successively. 

Evaluation. — All three must be named, but slight 
errors, such as " money," " pennies," for " a 
penny," are allowable. 

6. Describing Pictures. 

Materials. — Binet's three pictures — chosen as con- 
taining people, and suggesting a story, and having 
a certain standardised difficulty. 

There can, I think, be little doubt that pictures 
(1) better printed, (2) larger, (3) coloured, (4) re- 
presenting actions in progress, (5) showing children, 
would be much more appropriate than Binet's 
original engravings. But these alone have been 
standardised. 

Instructions. — " Look at this picture and tell me 
all about it." Binet's instructions are : " What is 
this ? " and if the child says, " A picture," " Tell 
what you see there." It is better, however, to 
avoid leading phrases like " What can you see in 
it ? " (which rather suggests enumeration) and 
" What are they doing ? " (which suggests inter- 
pretation). Repeat instruction once for each pic- 
ture, if there is no answer. Words of praise or 
encouragement alone may be added : " Isn't it a 
pretty picture ? . . . Do you like it ? " Or even 



BINET'S TESTS OF INTELLIGENCE 53 

" That's right ! " if the child is on the point of 
saying something but is withheld by shyness. 

Evaluation of replies. — 

Record the type of response given to the first 
picture ; if doubtful, use the second and third and 
record the type of response most frequently given, 
i. e. employed for two pictures out of the three. 
Binet distinguishes three types of response corre- 
sponding to three stages of development. 

A. Enumeration (E.). (Age 3.) E.g. — 

i. " A man, boy." 
ii. " There's an old man and a lady," 

etc. (mere list of objects or details), 
iii. " I can see a room with a chair, a 

table, and a looking-glass, and there's 

a man and a sofa." 

Two items at least should be enumerated. 
If the child only gives one, do not ask, 
" Anything else ? " but proceed to another 
picture. 

B. Description (D.). (Age 6.) (Phrases indicat- 

ing actions or characteristics.) 

i. " They're pulling a cart." 
ii. "A man and a woman sitting on a 

seat." " An old man asleep." 
iii. " A man standing on a bed and trying 

to look out of the window." " A 

man looking at himself in the 

glass." 



54 MENTAL TESTS 



C. Interpretation (I.). (Age 12.) (Goes be- 
yond what is actually visible in the picture 
and mentions the situation or emotion it 
suggests.)' 

i. " They're moving," " they've a heavy 
load," " they can't pay their rent." 
ii. "Miserable," "poor," "have no 
home," " the man is saying his 
prayers," " his daughter " or 
" wife " (looking after him, etc.). 
iii. " A prisoner," " he wants to get out," 
" he's trying to see what's in the 
yard," " he is lonely " or " think- 
ing," " a rag-picker," " a man in 
trouble," " a man on board ship." 

Age Four 

7. Repeating Syllables. 

Instructions. — " Listen again, and say this after 
me." (The phrases should be pronounced deliber- 
ately and with expression. Begin with no. iii. ; 
but if the child remains silent the examiner may 
give him first a shorter sentence (i. or ii.), and then 
apparently try iii. again.) — 

i. (2 syllables). " Father." 
ii. (4 syllables). " My hat and shoes." 
iii. (6 syllables). " I am cold and hungry." 

(Age 4.) 
iv. (8 syllables). "Here is the cloth ; my hands 

are clean." 
v. (10 syllables). " His name is Jack : he's 

such a naughty dog." (Age 5.) 



BINET'S TESTS OF INTELLIGENCE 5$ 

vi. (12 syllables). " It is raining outside ; but 

we can stay indoors." 
vii. (14 syllables). " While Jack was doing his 

lessons, I caught a little mouse." 
viii. (16 syllables). "We are going for a walk: 

Mary, let me see your pretty hat." (Age 7.) 

xiii. (26 syllables). " The other morning I saw 
in the street a little yellow dog. Little 
Maurice has spoilt his new apron." 
(Age 14.) 

Evaluation. — Allow no error at all, except mis- 
pronunciations due to speech defects. (Binet's 
sentences appear to have been deliberately com- 
posed of two clauses. This seems unfortunate, as 
even an intelligent child may forget one. In trans- 
lating them I have endeavoured to keep the general 
sense of the original, while making the phraseology 
more natural for a child.) 

8. Repeating Numbers. 

Instructions. — " Listen. Say these numbers after 
me"— 

(For use only after failure in first set.) 
714 286 539 

Evaluation. — (See Test 2.) 

9. Counting Pennies. 

A. Four Pennies. (Age 4.) 

Materials. — Four pennies placed in a row. 

Instructions. — " Do you see these pennies ? 
Count them, and tell me how many there are." 



56 MENTAL TESTS 

If the child at first answers at random, add : 
" Count them aloud, and point to each penny as 
you count it " ; but do not demonstrate. (It may 
be of interest to see if the child can do it when 

shown : " Count like this : one, two " touching 

the first two with the finger as each is counted. 
But do not use his answer for strict comparisons.) 

Evaluation. — The first random answer does not 
count. 

B. Thirteen Pennies. (Age 6.) 
Instructions, etc., as before. 

10. Comparing Two Lines. 

Materials. — Two parallel horizontal lines, 5 cm. 
and 6 cm. respectively, previously drawn in ink on 
a card or paper, the longer 3 cm. below the shorter, 
with its centre under that of the other. 

Instructions. — " Do you see these lines ? Tell 
me which is the longer ? " 

Evaluation. — No hesitation is allowed. (Some 
investigators allow the examiner to repeat the in- 
struction : English children will often respond 
more readily to the injunction : " Put your finger 
on the long one." But Binet insists that the child 
shall not only perceive the difference, but also 
understand, without any further help, that the 
phrase " the longer " implies making a comparison.) 

11. Comparing Faces. 

Materials. — Binet's six faces. Show only two at 
a time. 



BINET'S TESTS OF INTELLIGENCE 57 






-O 



705 



(Lo 



Us "^ 

r 






% 



%& 








58 MENTAL TESTS 

Instructions. — " Which is the prettier of these 
two faces ? " (If " prettier " seems not to be under- 
stood, "prettiest" or "Which do you like the best 
of these two ladies ? " "Which is the nice one ? " 
may evoke correct answers. But these should not 
be counted for purposes of strict comparisons.) 

Method. — It is better to cover the lower pairs or 
pair while dealing with the first or second. 

Evaluation. — All three comparisons must be cor- 
rectly made. Repeat the questions once if necessary. 



Age Five 

12. Performing Three Commissions. 

Materials. — Key, book, etc. Arrange the room 
while the child is carrying out one of the drawing 
or writing tests. 

Instructions. — "Do you see this key? Go and 
put it on the table there. Then shut the door. 
And after that bring me the book on the chair near 
the door. Do you understand ? First, put the 
key on the table, then shut the door, then bring 
me the book." (Note repetition of instructions. 
Do not let the child commence until this is com- 
pleted.) 

Evaluation. — All three commissions must be per- 
formed spontaneously without any further instruc- 
tion or hint (" Well, and now ? " " What have you 
forgotten ? "). 



BINET'S TESTS OF INTELLIGENCE 59 

13. Draws from Copy. 

A. A Square. (Age 5.) 

Materials. — A square, each side measuring about 
3 to 4 cm., drawn beforehand in ink, preferably on 
a card. Plain paper. Pen and ink (deliberately 
advised by Binet, making the task more difficult. 
Most American adapters recommend pencil.) 

Instructions. — " I want you to copy this for me " 
(pointing to square). " Draw it here " (handing 
pen and paper). (If encouragement is needed : 
" What do you think this shape (picture) is ? See if 
you can draw it." Do not use the word " square " 
yourself.) 

Evaluation. — Passes if it can be recognised as an 
attempt at a square. If one side is twice the other, 
if the lines cross considerably at the corners or bend 
round without any angles, the drawing fails. The 
size does not matter. (Allow only one attempt.) 
Should take about one minute. 

B. A Rhombus or Diamond. (Age 6.) 

Materials. — A " diamond," about 7 cm. long 
and 4 cm. high, with sides 4 cm. long, drawn as 
before on a card. Paper, pen and ink. 

Instructions and Evaluation. — As before. Binet 
apparently requires at least one pair of opposite 
angles to be fairly equal, at least one pair of adjacent 
sides to be fairly equal, and the vertical diameter to 
be long. Absolute parallelism of the opposite sides 
is not insisted upon. The pass-standard is thus con- 
siderably below what an uninstructed teacher would 



6o MENTAL TESTS 

be apt to accept as a satisfactory reproduction. 
(Reference should be made to his samples.) 

14. Repeating Syllables. 

(10 syllables.) " His name is Jack : he's such a 
naughty dog." 

Instructions and Evaluation. — (See Test 7, no. v.) 

15. Giving Age. 

Instruction. — " How old are you ? " 

Evaluation. — Child should give his age in years, 
last birthday. Note : children very often say 
" seven " when they mean " getting on for seven." 
Hence, if the first answer is wrong, ask specifically 
" How old were you last birthday ? " Parents also 
often give an infant and a child about to leave 
school an age above the true one : and dull children 
(except when about to leave) an age below the real 
one. The child's answer should be accepted if it 
corresponds with what it has commonly or recently 
been told. Do not, therefore, insist too rigidly on 
the age given by the birth certificate or the register. 

16. Distinguishing Morning and Afternoon. 

Instructions. — " Is it morning or afternoon now ? " 
(in the morning). Or, " Is it afternoon or morning 
now ? " (in the afternoon). 

Evaluation. — Repeat the question if there is any 
possibility of the child having merely echoed one 
of the words thoughtlessly. (Asking " Have you 
had your dinner yet ? " elicits answers interesting 
to compare with the above.) 



BINET'S TESTS OF INTELLIGENCE 61 

17. Naming Four Primary Colours. 

Materials. — Four oblong pieces of paper, 2x6 
cm., coloured bright red, yellow, blue and green, 
and gummed beneath one another on a card. 

Instructions. — " What colour is this ? " pointing 
to each in turn. 

Evaluation. — No error is allowed. Should take 
about 6 seconds. But the time limit does not appear 
to be strictly enforced. 

18. Repeating Numbers. 

Instructions. — " Listen. Say these numbers after 
me." 

(For use only after failure in first set.) 
3681 5749 8526 

Evaluation. — (See Test 2.) 

19. Comparing Two Weights. 

Materials. — Four small similar boxes (about 
1*5 x 2*5 x 3*5 cm.) weighing 3, 12, 6 and 15 grammes. 

Instructions. — " You see these boxes (showing 
first the pair weighing 3 and 12 grammes placed 5 or 
6 cm. apart). Tell me which is the heavier." 

If the child merely points, add, without any 
gesture : " Take them in your hands and weigh 
them." (English children respond better to the 
instruction " Lift them " or " Feel them." " And 
give me the heavy one." But do not use the 
modification if strict comparability is required. 
Kuhlman and the Stanford Revision allow a demon- 
stration : Binet and Yerkes prohibit it.) In any 



62 MENTAL TESTS 

case do not put them in his hands. If he merely 
lifts one, or both together, do not correct him. If 
there is any doubt with the first pair, repeat the 
experiment with the second pair (6 and 15 grammes) ; 
and then with the first pair again. (If the child 
fails to understand, it is interesting to put them 
successively into his hand, and ask, " Which is the 
heavier ? " But his response in this case does not 
count.) For the second and third trials use the 6 
and 15 gramme weights and then the first pair again. 

Evaluation. — All three trials must be correct : if 
any doubt continue repetitions. 

20. Giving Number of Fingers. 

Instructions. — " How many fingers have you on 
your right hand ? " " And how many on your left 
hand ?"..." How many does that make on both 
hands altogether ? " 

Evaluation. — The replies must be made without 
stopping to count : and all three questions must be 
correctly answered. 

Age Six 

21. Counting Pennies. 

A. Thirteen Pennies. 

Materials. — Thirteen pennies placed in a row. 
Instructions and Evaluation. — (See Test 9, B.) 

22. Drawing from Copy. 

B. A Rhombus or Diamond. 

Instructions and Evaluation. — (See Test 13, B.) 



BINET'S TESTS OF INTELLIGENCE 63 

23. Transcription. 

Materials. — " See little Paul " written in a bold, 
copy-book handwriting on a card or sheet of paper. 
Paper, pen and ink. 

Instructions. — " Will you copy that for me ? " 

Evaluation. — The test is passed if the copy is 
sufficiently legible to be read by a person who did 
not know what was to be written. 

24. Naming Days of the Week. 

Instructions. — " Can you tell me what are the 
days of the week ? " 

Evaluation. — The days must be named in order 
without error or hesitation, in 10 seconds. 

25. Naming Coins. 

Materials. — Nine coins, all placed in a row on the 
table with the head upwards : similar coins should 
not be adjacent. Order upon table : is., id., 6d., 
Id., 2s., \d., £1, 2s. 6d., 10s. Order of difficulty : id., 
Id., \d., is., 6d., 2s., £l, 10s., 2S. 6d. (3^., 5^., 4J.). 

(One pound and ten-shilling notes must be allowed.) 

Instructions. — Ask " What is this ? " pointing to 
each in succession. Neither examiner nor child 
should handle them or turn them over. 

Evaluation. 

A. Four Commonest Coins. (Age 6.) 
(is., 6d., id., r^d.) No error allowed. 

B. Nine Commonest Coins. (Age 9.) 

All should be named correctly in 40 seconds. If an 
error is attributable to passing confusion, Binet 



64 MENTAL TESTS 

allows a second trial of the whole series after a few 
minutes. (An interesting variant is to ask what 
coins there are larger than a shilling, before passing 
to B.) 

26. Reconstructing Divided Oblong. 

Materials. — Two cards (4*5 x 7*5 cm.), one in- 
tact, the other divided along one diagonal into two 
equal triangles. Place the triangles so that the 
longest sides are at right angles, but do not face 
towards each other. 

Instructions. — " One of my cards has been cut 
in two ; can you put the pieces together again, to 
make a whole one, like this ? " 

If the child merely looks at the cards without 
touching them, say : " Move them about and see 
if you can fit them together," and, if necessary, place 
one in his hand. 

See that the child does not turn one triangle over. 
(Before cutting the card, black one side all over. 
This does not appear to alter the difficulty of the 
test, but prevents turning over.) If the child 
makes a wrong combination and appeals for judg- 
ment, give no opinion. Remain silent, or say 
merely, " What do you think ? " 

27. Defining Concrete Terms. 
Instructions. — " What is — 

(1) a fork ? 

(2) a table ? 

(3) a chair ? 

(4) a horse ? 

(5) a mother ? " 



BINET'S TESTS OF INTELLIGENCE 65 

(A word commonly used by other investigators 
is " kitten," or " cat " : " fork " is unfortunately 
a difficult word to begin with.) For shy or silent 
children : " You know what a fork is, don't you ? 
Well, tell me what it is — what is a fork ? " " You 
have seen a horse, haven't you ? Tell me what a 
horse is." The instructions may be repeated, but 
use no other form of words. (Give the child a 
minute to reply in.) 

Evaluation of Replies. — The character of three 
replies out of five determines the value of the test. 
The variations in the age assignments of definition 
superior to use depend largely on the inclusion of 
such replies as ii., (1), (3), (4) and (7) under i. 
rather than under ii. 

Note " U " or " G " according as child defines — 

i. In terms of Use. (Age 6.) 

(1) What you eat with. 

(2) Something to have your dinner on : 

where the plates are put. 

(3) It draws a cart. 

(4) She takes care of the babies. 

ii. In terms superior to Use (by Genus with or 
without Differentia, or by Description). 
(Age 10.) 

(1) A thing to sit on : something that you 

eat with. (" Thing " and " some- 
thing," however, are not accepted 
for " horse " or " mother.") 

(2) An instrument. 

(3) It has four legs : it's silver. 



66 MENTAL TESTS 



(4) A piece of wood, part of the furniture. 

(5) An animal. 

(6) A lady. 

(7) One who cooks our dinners. 

(Note : if a child uses " thing " or " some- 
thing " for " chair," I then give " mother " and 
"horse," otherwise even a bright child, having 
given "thing" for "chair," "table" and "fork" 
without correction is apt from sheer inertia to 
offer " thing " as the genus of " horse.") 

iii. Merely repeating the word, or pointing to 
the object is marked a failure, without 
(apparently) giving the child a further 
chance. 

28. Repeating Numbers. 

Instructions. — " Listen. Say these numbers after 
me." 

(For use only after failure in first set.) 
52947 63852 973 18 

Evaluation. — (See Test 2.) 

29. Describing Pictures. 

Description (D.) (Phrases indicating actions and 
characteristics.) 

Instructions and Evaluation. — (See Test 6, B.) 

30. Distinguishing Right and Left. 

Instructions. — " Which is your right hand ? " 
..." Which is your left ear ? " 

Evaluation. — The child must perform both cor- 
rectly without any kind of help. Hesitation and 



BINET'S TESTS OF INTELLIGENCE 67 



self-correction (without any hint) are allowed : if 
by a slip the child shows his left hand or right ear, 
the experimenter waits a moment for a spontaneous 
correction, which is allowed to pass, but his manner 
of waiting should not suggest that the first action 
was wrong. 




Age Seven 

31. Recognising Missing Features. 

Materials. — Binet's four pictures of faces without 
mouth, nose, eye, and of body without arms. 
Instructions. — " Look at this lady's face. Can 



68 MENTAL TESTS 

you tell me what has been left out ? " (Begin with 
face without mouth.) 

If the child says, " Her body," reply, " Oh, I was 
only trying to draw her face. What must I put in 
to finish the drawing of her face ? " (" What have 
I forgotten in drawing her face ? ") 

Evaluation. — Three correct answers out of four 
are required. 

32. Adding Three Pennies and Three Halfpennies. 
(Concrete.) 

Materials. — Three pennies and three halfpennies 
set out in a row. (American investigators commonly 
use stamps, but to many children the value of these 
is unfamiliar.) 

Instructions. — " Will you count this money for 
me, and tell me how much there is altogether ? " 

Evaluation. — No error and no repetition of the 
instruction is allowed. The test should be done 
in 8 to 10 seconds. " It is useless to wait 15 
seconds." 

33. Stating Differences between Concrete Objects. 

Instructions. — " You know what wood is, don't 
you ? . . . And you know what glass is ? . . . They 
are not the same, are they ? ... In what way are 
they not the same ? " (I would add, if child 
hesitates : " They are different, are they not ? 
Well, do you think you can tell me what the dif- 
ference is ? . . . How can you tell ' glass ' from 
< wood ' ? ") 



BINET'S TESTS OF INTELLIGENCE 69 

The following words are suggested by Binet — 

i. fly, butterfly; 
ii. wood, glass ; 
iii. paper, cardboard. 

Evaluation. — Two out of three statements must 
be correct. Any true difference will pass, though 
trivial. But if the child repeats the same differ- 
ence, e. g. " It is larger," it is insufficient. (Ask, 
" In what other way are they not the same ? ") 
Often a child takes a minute : but if he takes 
longer than 2 minutes for all he fails. 

34. Repeating Syllables. 

(16 syllables.) "We are going for a walk: Mary, 
let me see your pretty hat." 

Instructions and Evaluation. — (See Test 7, no. 
viii.) 

35. Writing from Dictation. 

Materials. — Pen, ink, paper. 

Instructions. — " Will you write this down for me 
on this piece of paper ? " 

" The pretty little girls." 

Evaluation. — The writing ( ? and spelling) must 
be sufficiently legible and accurate to be read by a 
person who did not know what was to be written. 



jo MENTAL TESTS 

Age Eight 

36. Reading and Reproduction. 

Material. — Translation of Binet's passage, printed 
or typed, with English place-names and money- 
values substituted for the French. 

Three / Houses / on Fire./ 
London, / September 5th. / A huge fire / last night/ 
burnt down / three houses in the middle of the 
city. / Seventeen families /now have no homes. /The 
loss is more than 15,000 pounds. /A young barber,/ 
who saved /a baby / in its cradle, / was badly / hurt/ 
about the hands./ 

Instructions. — " Will you read this for me, 
please ? " Two seconds after reading is finished, 
remove the passage, and say : " Tell me what you 
have been reading about." 

Evaluation. — Each correct phrase or word as 
indicated above constituted one item. 

A. Recalls two items. (Age 8.) 

B. Recalls six items. (Age 9.) 

37. Answering Easy Questions. 
Instructions. — " Tell me this — 

(1) Suppose you are going somewhere by train. 

What must you do if you miss your train ? 

(2) Suppose one of the other boys (girls) hit you 

by accident — without meaning to. What 
should you do ? 

(3) Tell me what you ought to do if you broke 

something that belonged to somebody else I " 



BINET'S TESTS OF INTELLIGENCE 71 

If no answer is given, repeat the question as usual, 
not sternly, but pleasantly, prefixing : " Did you 
catch what I said ? " Do not vary the wording. 

Evaluation. — Two out of three must be answered 
satisfactorily. 

(1) Satisfactory answers. — " Wait for another " — 

" Take the next." 
Unsatisfactory answers. — " Go home again " 
— " Run after it " — " Try not to miss it." 

(2) Satisfactory answers. — " Do nothing " — " For- 

give him." 
Unsatisfactory answers. — " Tell teacher " — 
" Hit him back." 

(3) Satisfactory Answers. — " Pay for it " — " Own 

up "— " Buy another " — " Ask to be for- 
given " — " Say I was sorry." 

Unsatisfactory answers. — " I should cry " — 
" Hide it." 

38. Counting Backwards 20-0. 

Instructions. — "You can count, can't you — 1, 2, 
3, and so on ? Now do you think you could count 
backwards ? Start at 20, and go on till you reach 
I." (If the child does not understand :) " Count 
like this : 20, 19, 18 " (proceed no further). 

(Yerkes suggests that the experimenter always 
count from 25 to 21, and then pause for the examinee 
to continue.) 

Evaluation. — One error (either of omission or 
inversion) only is permitted (Binet allows 20 seconds). 
The child who thinks out the numbers by counting 
up from 1 each time fails. 



72 MENTAL TESTS 

39. Giving Full Date. 

Instructions. — " What is the date to-day ? " (If 
the word " date " is not understood, ask in detail : 
" What day of the week is it to-day ? " " What 
month is it ? " " Do you know what day of the 
month?" [ist, 2nd, 3rd, or] "what number?" 
" And what is the year — nineteen what ? ") 

Evaluation. — All four items must be correctly 
given : but an error of three days either way is 
allowable for the day of the month (unless that 
involves an error in naming the month). 

40. Giving Change. 

Materials. — The current coins \d., \d., id., 6d., 
2s., 2s. 6d., ios., £1 and is., and in addition three 
pennies and the three halfpennies. The five 
boxes used for the weights. 

The shilling is kept by the experimenter to pay 
for the box. 

The rest, with the boxes, are placed near the child. 

Instructions. — " Now, shall we play shop for a 
change ? You shall be the shopkeeper. Here are 
some boxes for you to sell ; and here is your money. 
See how rich you are ! Now, will you sell me one of 
your boxes, please ? How much are they each ? 
Twopence, shall we say ? Well, here is a shilling. 
Can you give me the right change, please ? " (The 
examiner holds out his hand for the money.) 

Evaluation. — The child must actually hand over 
the right amount (sixpence and fourpence in pennies 
or halfpennies) : merely stating it correctly does 
not count. 



BINET'S TESTS OF INTELLIGENCE 73 

Age Nine 

41. Repeating Numbers. 

Instructions. — " Listen. Say these numbers after 

me"- 

(For use only after failure in first set.) 
250634 5 7 3 9 ! ^ 495827 

Evaluation. — (See Test 2.) 

42. Naming Months. 

Instructions. — " Can you tell me what are the 
months of the year ? " 

Evaluation. — Binet allows 15 seconds, and one 
error. 

43. Naming Coins. 
Nine Commonest Coins. 

Instructions and Evaluation. — (See Test 25, B.) 

44. Reading and Reproduction. 
Recalls Six Items. 

Instructions and Evaluation. — (See Test 36, B.) 

45. Defining Concrete Terms. 
Superior to Use (G.). 

Instructions and Evaluation. — (See Test 27, no. ii.). 

46. Arranging Five Weights in Order. 

Materials. — Five boxes, identical in colour, shape 
and size (about 1*5 x 2*5 x 3*5 cm.), and loaded 
with shot and cotton wool to weigh 3, 6, 9 and 



74 MENTAL TESTS 

15 grammes, without rattling. The key letters, B, I, 
N, E, T, may be written in order on the bottom of 
the boxes. 

Instructions. — " Do you see these boxes ? They 
all look the same, don't they ? But they don't 
weigh the same. Some are heavy, and some are 
light. I want you to find the heaviest of all, and 
put it here. Then find the one which is nearly 
as heavy, and place it next. Then the one which 
is still less heavy ; then the one which is lighter still ; 
and, last of all, the one which is lightest of all, here." 

Allow three trials if necessary, mixing the boxes 
up first. 

Evaluation. — The arrangement must be abso- 
lutely correct in two out of three trials, and the 
whole accomplished in 3 minutes. It is of special 
interest to record the subject's actual arrangement. 

47. Sentence Building with Three Words. 

Materials. — Paper, pen and ink: and a card 
with " London, river, money " written on it. 

Instructions. — " I want you to make up a sentence 
for me with these three words in : London, river, 
money." 

Instead of " London " it is often customary to 
employ the nearest town that is on a river. (Most 
American investigators, following Goddard, conduct 
this test orally.) 

Evaluation. 

A. Two distinct ideas or sentences given (indi- 
cates mental age of 10). " London has 
money and rivers." 



BINET'S TESTS OF INTELLIGENCE 75 

B. One idea or sentence given (indicates mental 

age of 1 1), e. g. " In the river at London 
I found some money." A set of sen- 
tences in which the thought is well 
co-ordinated into a unitary story or 
description passes. 

C. Three distinct ideas or sentences consti- 

tuted a failure. E. g. " London is a 
town. There is a big river. Some people 
have money." 

Enter "1," "2" or "3" according to number 
of sentences given, and note time. At least three- 
quarters of the test should be written within a 
minute. Binet states that this is one of the rare 
cases in which a child may succeed by having heard 
of the test from another child. If there is any 
likelihood of this, ask at the outset : " What do you 
think I have been asking the others to do with these 
words ? " and substitute others, if necessary. The 
child may guess the test from school exercises. 

48. Drawing Two Designs from Memory. 

Materials.— Binet's two designs, drawn pre- 
viously on a single card or sheet, kept out of sight 
until required. A pencil and plain paper. 




Binet's list No.4*S. 



76 MENTAL TESTS 

Instructions. — " I am going to show you two 
easy drawings. I want you to look at them very 
carefully until I take them away. Then, after I 
have turned them over, see if you can draw them 
both from memory on this paper. You will only 
see them for a very few seconds. Now look at 
them both carefully first of all. Ready ? Now ! " 
The drawings are held steadily in front of the child, 
the truncated prism on the left, for 10 seconds (see 
that the child does not imagine he has to copy them 
at once), and then taken away and turned face down- 
wards. " Now try and draw them for me here." 

Evaluation. — The whole of one and a half of the 
other must be reproduced fairly exactly. No 
second attempt is allowed. Neatness of drawing 
does not count. The examiner must be careful 
not to interpret " fair exactness " more strictly for 
older than for younger children. The standard 
accepted in the case of this test is thus far below 
what the uninstructed teacher would accept as a 
satisfactory reproduction. 

Age Eleven 
49. Explaining Absurdities. 

Instructions. — " Listen carefully to what I am 
going to say. There is something in it that is 
really quite silly and impossible. See if you can 
tell me what is wrong." 

i. " ' One day, a man fell off his bicycle on to his 
head and was killed instantly. He was taken 
to the hospital and they say he will never 
get better.' What is there silly in that ? " 



BINET'S TESTS OF INTELLIGENCE yj 

ii. " ' Once the body of a poor girl was found 
in a wood, cut into eighteen pieces. They 
say that she killed herself.' What is silly 
in that ? " 

iii. " ' Yesterday there was a railway accident. 
But the newspaper says it is not a serious 
one, as only forty-eight people were killed.' 
What is silly in that ? " 

iv. " * I have three brothers — Jack, Tom and 
myself.' What is silly in that ? " (Female 
examiners must preface this with, " A boy 
said to me, etc.," or else substitute, " I have 
three sisters, Jane, Mary and myself.") 

v. " ' A man once said, " If I should ever grow 
desperate and kill myself, I shall not choose 
a Friday to do it on, for Friday is an un- 
lucky day, and would bring me bad luck." ' 
What is foolish in what the man said ? " 

Evaluation. — Three absurdities should be de- 
tected out of five. If a child's first statement is 
not clear (e. g. " myself is silly " in answer to iv.), 
say, " Explain what you mean." Otherwise, give 
him no second chance. 

(i.) Correct : " He couldn't get well if he was 
already dead." " First you said he was 
dead, and then you said he wouldn't get 
well again." 
Incorrect ; " They ought to have taken him 
to the mortuary." " If he fell off his 
bicycle, he wouldn't fall on his head." 
(ii.) Correct : " You can't cut yourself into 
eighteen pieces." " If she killed herself 
she couldn't cut herself up." 



78 MENTAL TESTS 

(iii.) Correct : " It must have been serious if 
forty-eight were killed, or if anybody was 
killed." " If it wasn't serious only one 
or two would have been killed." " Forty- 
eight isn't serious in war-time." 

Incorrect : " Forty-eight people couldn't be 
killed in a railway accident." 
(iv.) Correct : " You have only two." " You are 
not your own brother." " You shouldn't 
count yourself." 

Incorrect : " You should put yourself last." 
(v.) Correct : " If he killed himself, the day 
wouldn't matter." " He couldn't have 
bad luck if he was dead." " If he was 
desperate, he wouldn't wait till Friday." 

Incorrect : " He is silly to believe in bad luck." 
" Friday isn't different -fee any other day." 

50. Answering Difficult Questions. 
Instructions. — " Can you tell me this ? " 

(1) " What should you do if you found you were 

late on your way to school ? " 

(2) " Suppose a boy does something that is un- 

kind : why do we forgive him more readily 
if he was angry than if he was not angry ? " 

(3) "If some one asked what you thought of a 

boy (or girl) whom you did not know very 
well, what should you say ? " 

(4) " Why should we judge a person by what he 

does, and not by what he says ? " 

(5) " Suppose you were going to undertake some- 

thing very important : what should you 
do first of all ? " 



BINET'S TESTS OF INTELLIGENCE 79 

Repeat a question once, if necessary, but do not 
vary the wording. 

Evaluation. — Allow 20 seconds for reflection on 
each question. Three out of five must be answered 
satisfactorily. 

(1) Satisfactory: "Hurry" or "Run" ("Go 

straight to school " may be accepted if it 
appears that the child sometimes plays or 
carries out errands on its way). 
Unsatisfactory : " Get the stick." " Leave 
earlier." " Get up sooner next time." 
" Ring the bell." " Get a note to excuse 
me." By convention, anything not em- 
bodying the idea of hurrying. 

(2) Satisfactory : " Because he didn't know what 

he was doing." " Because he'd be sorry 
afterwards." Anything suggesting that 
anger may constitute an excuse, however 
badly expressed. 
Unsatisfactory : " He oughtn't to get angry." 
Anything suggesting disapproval of anger. 

(3) Satisfactory : " I could not say anything." 

" I could not tell him without finding out." 
" I should say, ' I do not know.' " 
Unsatisfactory : " I should have to ask." 
" Say I did not know his name." Usually 
unintelligible. 

(4) Satisfactory : " You can rely on his actions, 

but not on what he says." " Because 
he might not always speak the truth." 
" Actions speak louder than words." 
Unsatisfactory : Usually unintelligible. " Be- 
cause you can't tell." " You ought to 
speak the truth." 



80 MENTAL TESTS 

(5) Satisfactory : " Think it over." " Ask some 
one about it." " Prepare for it." 
Unsatisfactory : Usually unintelligible. " Not 
do it." 

(Some say " Tidy myself," " Put on a clean collar ; " 
in that case make it clear that you mean doing some- 
thing important, not going somewhere important.) 

51. Repeating Numbers. 

Instructions. — " Listen. Say these numbers after 
me." 

(For use only after failure in first set.) 
9647518 4829653 5928136 

Evaluation. — (See Test 2.) 

52. Giving Sixty Words in Three Minutes. 

Instructions. — " I want you to give me as many 
words as you possibly can in 3 minutes. Keep 
saying words like this till I stop you : school, teacher, 
board, boy, girl, and so on. Some children can 
give more than 200. Are you ready ? Now start." 
When he stops encourage him immediately by say- 
ing : " Very good. Keep on." 

Evaluation. — Sixty words must be given, ex- 
clusive of repetitions. If the child gives sentences, 
start him again, saying: "You must give separate 
words." Be careful (1) to note the time, if possible 
with a second hand (2) to count the words, entering 
a stroke or other mark for each, and calculating the 
total. It is interesting to record the key-words of 
the child's various topics ; it is seldom possible to 
put down all words. 



BINET'S TESTS OF INTELLIGENCE 81 

53. Sentence Building with Three Words. 

Materials. — Paper, pen and ink, and a card with 
" London, river, money," written on it. 

One Idea or Sentence. 

Evaluation. — (See Test 47, B.) 

Age Twelve 

54. Giving Three Words to Rhyme. 

Instructions. — " Do you know what a rhyme is ? 
When two words end the same way, we call them 
rhymes. ' Jill ' rhymes with ' hill ' because they 
both end in ' ill.' Do you understand ? Now can 
you give me three words which rhyme with 
< obey ' ? " 

Evaluation. — -The child must give three genuine 
words that rhyme in 1 minute. Binet's instruc- 
tions to the child ask for " other words " or " all 
the words." It saves time to specify three to the 
child. If the child gives nothing, or has not given 
enough, urge him by saying " what (else) rhymes 
with ' obey.' " Apparently " disobey " may be 
accepted as one of the three. 

55. Rearranging Mixed Sentences. 

Materials. — Three cards containing the following 
words — 

i. a defends dog good his bravely master ; 
ii. my have teacher I the correct asked paper to ; 
iii. home we early our in country left visit the to 
friends. 

G 



82 MENTAL TESTS 

Instructions. — " Put these words in order, and 
find out the sentence which they make." 

Evaluation. — Two correct solutions must be given 
out of three. Only I minute is allowed for each. 

Correct solutions are — 

i. " A good dog defends his master bravely." 
" A dog defends his good master bravely." 
(" A master defends his good dog bravely," 
is, according to Binet, " poor " and appar- 
ently incorrect), 
ii. " I have asked my (the) teacher to correct 
the (my) paper." 
(" I asked my teacher to have the paper 
correct" is, presumably, incorrect.) 
iii. " We left home early to visit our friends in 
the country." 
(" We left our friends in the country to visit 
our home early," and other sensible variants 
are presumably correct.) 

56. Describing Pictures. 

Interpretation. — (Goes beyond what is actually 
visible in the picture, and mentions the situation or 
emotion it suggests.) 

(See Test 6, C.) 

Age Thirteen 

57. Resisting Suggestion. 

Materials. — A book of six leaves with two lines 
drawn in the same straight line on one page in 
opening. The lengths must be as follows — 



BINET'S TESTS OF INTELLIGENCE 83 





1st line. 


2nd line. 




1st page 


4 cm. 


5 cm. 




2nd page 


5 cm. 


6 cm. 




3rd page . . 


6 cm. 


7 cm. 




4th page . . 


7 cm. 


7 cm. 




5th page . . 


. - . 7 cm. 


7 cm. 


* 


6th page 


7 cm. 


7 cm. 





Instructions. — For the first three pages : " Which 
is the longer of those two lines ? " for the last three, 
without changing the tone : " And these ? " 

Evaluation.- — Note whether child's judgments 
are right or wrong in each case, especially with 
reference to the last three. The child succeeds 
if he judges two out of three equal lines to be 
equal. 



58. Solving Circumstantial Problems. 

Instructions. — " Can you guess the answer to this 
riddle ? 

i. " One day a woman, walking in Epping Forest, 
stopped still, terribly frightened. Then she 
hurried to the nearest police station, and 
told the policeman she had just seen, hang- 
ing from the branch of a tree, a well, 

what do you think it was she saw ? " 
ii. " My next-door neighbour has had three 
visitors. First, a doctor called ; then a 
lawyer ; and then a clergyman. What do 
you think has been happening there ? " 

Evaluation. — Both questions must be correctly 
answered. 



84 MENTAL TESTS 

i. Correct: Replies must contain the idea of 
some one hanged. If the child answers 
" a man," " a dead person," therefore, ask 
" How did he get up in the tree ? " 
Incorrect : " A bird." " Some one robbing a 
nest." 

ii. Correct: "Some one is dying," "is very 
ill." (Severe illness can be inferred from 
the visit of the doctor alone. But Binet 
apparently accepts it, without inquiring 
whether the child knows the object of the 
other visitors.) 



Age Fourteen 

59. Repeating Syllables. 

(26 syllables.) " The other morning I saw in the 
street a little yellow dog." " Little Maurice has 
spoilt his new apron." 

Evaluation. — (See Test 7, no. xiii.) 

60. Defining Abstract Terms. 

Instructions. — " Can you tell me this ? What is 
meant — 

i. by kindness ? 
ii. by justice ? 
iii. by charity ? " 

(For " charity " some investigators have substi- 
tuted " obedience " : but this changes the difficulty 
of the test.) 



BINETS TESTS OF INTELLIGENCE 85 

Evaluation. — Two must be correctly defined out 
of three. Correct definitions — 

For (i) contain the idea of an instance of affec- 
tion, tenderness, politeness or consideration to 
others. (" Being polite or good to others " is 
correct. " Being kind," " doing something good," 
are inadequate.) 

For (ii) contain the idea of treating people accord- 
ing to their merits, or of protecting the innocent 
and their interests, or of punishing the guilty. 
E. g. " when you punish wicked people," " playing 
fair." 

For (iii) contain the ideas of (a) poor or un- 
fortunate people, and (b) of showing kindness. 
E. g. " when you give poor people some money," 
" giving alms." 



Age Fifteen 

61. Drawing from Imagination the Cuts in a 
Folded Paper. 

Materials. — Two sheets of paper about 6 inches 
square. A pencil. One sheet is folded in four like 
a letter ready for an envelope. In the middle of 
the edge which presents but a single fold, a small 
triangular notch, about 1 cm. deep, is drawn. 

Instructions. — " Here is a sheet of paper that has 
been folded across and then folded again. Suppose 
now Icut out a notch just here. When the paper 
is unfolded again, what would it look like ? Will 
you show me on this piece how and where it would 
be cut ? " 



86 MENTAL TESTS 

Evaluation. — Two diamond-shaped holes should 
be drawn in a line with each other, each in the middle 
of one half of the paper. 

62. Giving Differences between Abstract Terms. 

Instructions. — " What is the difference between — 

i. pleasure and happiness ? 
ii. poverty and misery ? 
iii. evolution and revolution ? " 

The words baggested by Binet {Bulletin) are — 

i. paresse, oisivete ; 

ii. evenement, avenement ; 

iii. evolution, revolution : and in 1908 scale also — 
iv. plaisir, bonheur ; 

v. orgeuil, pretention. 

Evaluation. — Two out of three must be cor- 
rectly answered. Good replies should bring out 
an opposition or antithesis between the differenti- 
ating ideas. E. g. (i) " happiness " is superior to 
or more general than " pleasure " ; (ii) should con- 
trast having little money with being in misery or 
pain ; (iii) should contrast slow change with sudden 
change. But Binet admits mere differences ; e. g. 
evolution is the movement of troops, revolution is 
an insurrection. 

63. Drawing the Displaced Triangle. 

Materials. — Paper and pencil for drawing. A 
card about 10 x 15 cm., cut across the diagonal, 
as used for divided card test, The card is first laid 



BINET'S TESTS OF INTELLIGENCE 87 

on the table before the subject with the cut edges 
touching. 




Instructions. — " Look carefully at the lower piece 
of this card. Suppose I turn it over and lay this 
edge (A-C) along this edge (A-B of the upper 
triangle), and suppose that this corner (C) is placed 
just at this point (B), what would it all look like ? 
Now I am going to take the piece away (remove 
lower triangle from view). Imagine it placed as 
I told you, and draw its shape in the proper position. 
Begin by drawing the outline of the top triangle." 

Evaluation. — The essential points are : (i) A C B 
must be preserved as a right angle ; (ii) A C must 
be made shorter than A B. 

64. Summarising Hervieifs Reflections on Life. 

Instructions. — " Attend carefully to what I am 
going to read you. When I have finished I shall 
want you to tell me the meaning of what I read in 



88 MENTAL TESTS 

your own words. The exact words that I use do 
not matter. Listen — 

' Many opinions have been given on the value of 
life. Some say it is good, others say it is bad. It 
would be truer to say that it is just medium. For, 
on the one hand, the happiness it brings us is never 
so great as we ourselves should like, and, on the 
other hand, the misfortunes it brings us are never 
so great as our enemies would want us to have. 
It is the intermediate nature of life that makes it 
fair, or, at least, prevents it from being altogether 
unfair.' 

Now see if you can give me, in your own 
words, the sense of what I have just read to you." 

Evaluation. — The central thought must be under- 
stood and these three ideas reproduced : (i) Life 
is neither good nor bad, but medium, for (2) it is 
not so good as we wish, but (3) better than what 
others wish for us. The terms and expressions 
matter little. 

65. Giving the Differences between President and 
King. 

Instructions. — " There are three chief differences* 
between a King and a President of a Republic. Can 
you tell me what they are ? " " Can you think of 
any of them ? " 

Evaluation. — Two of the following differences, 
apparently, must be given. (Some consider Binet 
required all of the first three.) 

i. A King inherits his crown : a President is 
elected. 



BINET'S TESTS OF INTELLIGENCE 89 

ii. A King is king for life : a President's term of 

office is limited, 
iii. The powers of a King are greater than those 

of a President, 
iv. A King is not directly responsible to the 

people : a President is. (Added by Melville 

in place of iii.) 

(This test is obviously more suited to French and 
American children than to English. The third 
difference is hardly true of an English king.) 



CHAPTER V 

burt's reasoning tests 

A teacher who has studied Binet's tests will at 
once perceive that they are unsuitable for the upper 
standards. They were not devised for the discovery 
of the bright children, but for the detection of the 
dull. If the aim is to select supernormal children 
to whom scholarships might be awarded, a more 
difficult series of tests — a series that appeals more 
exclusively to the higher mental functions — is 
necessary. The tests recently published by Mr. 
Cyril Burt and printed below were designed to meet 
that need. A full description of the circumstances 
under which the tests were drawn up and stan- 
dardised, together with an account of the develop- 
ment of reasoning in school-children, will be found 
in an article by Mr. Burt in the Journal of Experi- 
mental Pedagogy for June 191 9 and December 1919. 

To quote from that article : " The test-questions 
are intended to be given to each child individually 
and orally. In my own experiments each problem 
was type-written upon a separate card ; a fresh 
statement commenced on a fresh line ; and by 
means of indentation and spacing, question and 
premises were distinguished from each other. A 
card is handed to the child with the following 
instructions ; ' Will you read this little puzzle ? 

90 



BURT'S REASONING TESTS 91 

There is an easy question at the end. When you 
have read the question, read carefully again what 
is printed above, and try whether you can think of 
the answer.' The younger and duller children 
should read the test-questions aloud ; and with 
the youngest and dullest of all, the examiner should 
read the questions with or to the child. Children 
of higher levels (Standard III) need only read 
aloud the first few questions. Any child who is 
unable to read a particular word or to comprehend 
its meaning should be freely helped. The graver 
incongruities between difficulty of phrase and 
difficulty of logic have been eliminated. In a per- 
fectly revised list they should never occur. A bright 
young child is occasionally puzzled by such words 
as ' sub-tropical,' and ' emotion,' although com- 
petent to follow the reasoning. When it is clear 
that the child understands his task, he should be 
left quietly with the card, forgetful, if possible, of 
the examiner's presence. The emotional confusion, 
the ' examination paralysis,' that so commonly 
embarrasses an oral interview is by this means 
largely avoided. When the child gives an answer, 
it is invariably received with a word of praise, 
whether right or wrong ; and the child is asked 
to give his reason. 

" One mark is given for each test correctly answered 
and correctly reasoned. When necessary, the child 
may be given additional trials, not exceeding three 
in all for any one test. But for each unsuccessful 
attempt a quarter of a mark is deducted. A frac- 
tion — as a rule, a quarter, a half, or three-quarters 
respectively — is also deducted for an ill-expressed 
reason, an inadequate reason, or no reason at all, 



92 MENTAL TESTS 

In the cross-examination as to reasons lies the most 
valuable part of the test. The examiner gleans 
considerable information, not only about the know- 
ledge and intellectual procedure of the child, but 
also about its temperament and disposition so far 
as they affect his intellectual efficiency. In the 
final estimate of the child he would take into account 
both these broader observations, and in particular 
the speed with which the child has worked. In 
the actual marking no allowance is made for such 
latter factors ; nor is any time-limit assigned. 
Could scores be corrected on the basis of the general 
impressions incidentally gained, the correlations 
with ability, high as they are, would be still further 
raised. 

" For a child to work steadily through a series of 
fifty reasoning tests until he breaks down would, 
at any rate for the brighter and older children, be 
a slow and fatiguing process. A short series has 
therefore been constructed by selecting every third 
test in the full series. The short list thus contains 
only seventeen questions, two for each age except 
the first, which has three. 

" In the full list appended these selected questions 
are marked with asterisks. They have been more 
carefully chosen, more extensively used, and more 
thoroughly revised. For practical purposes, indeed, 
the short list will be sufficient, since this allows a 
rough and rapid determination of mental age. 
Where, however, it is required to obtain a more 
exact estimate of a child whose mental level is 
already approximately known — for example, in 
testing children within the same school standard — 
the full list is indispensable, since with the short 



BURT'S REASONING TESTS 93 

list no member of a fairly homogeneous class could 
be expected to differ from the others by more than 
one or two marks. 

" Children should be tested with the short list first. 
Even the oldest and brightest should begin with 
the easiest test. They should be carried through 
the series until they have broken down with three 
consecutive tests. The supplementary questions 
should be given subsequently, and upon a different 
day. Here it will be expedient to start, not at the 
beginning of the series, but about four tests below 
the level of the first serious failure made on the 
short list ; and the child should be carried through 
until he breaks down on at least six tests consecu- 
tively." 

BURT'S GRADED REASONING TESTS. 

Seven Years 

*i. Tom runs faster than Jim : Jack runs slower 
than Jim. Who is the slowest — Jim, Jack or Tom ? 

2. All wall-flowers have four petals : this flower 
has three petals. Is this a wall-flower ? 

3. It looks like rain : but I shall stay indoors. 
Shall I want an umbrella to-day ? 

*4. Kate is cleverer than May : May is cleverer 
than Jane. Who is the cleverest — Jane, Kate or May ? 

5. It is Sunday ; and on a Sunday afternoon Ada 
usually takes the baby out, or goes by herself to the 
pictures, or walks over to see her aunt, or else goes 
by tram to the cemetery. To-day she has no 
money with her : and the baby is asleep upstairs. 
Where do you think she has probably gone ? 

6. Tom said to his sisters : " Some of my flowers 



94 MENTAL TESTS 

are buttercups." His sisters knew that all butter- 
cups are yellow. So Mary said : " All your flowers 
must be yellow." Grace said : " Some of your 
flowers must be yellow." And Rose said : " None 
of your flowers are yellow." Which girl was right ? 
*7. I have bought the following Christmas pre- 
sents : a pipe, a blouse, some music, a box of 
cigarettes, a bracelet, a toy engine, a bat, a book, 
a doll, a walking-stick and an umbrella. My 
brother is eighteen : he does not smoke, nor play 
cricket, nor play the piano. I want to give the 
walking-stick to my father and the umbrella to my 
mother. Which of the above shall I give to my 
brother ? 

Eight Years 

8. All great men work hard and long every day : 
Sir John Smith worked three hours a day. Was 
Sir John Smith a great man ? 

9. Peter has a half-holiday on Wednesdays and 
Saturdays, and a whole holiday on Sunday. I am 
at work all day, except on Monday, Wednesday, 
Friday and Sunday. I want to take Peter to the 
tailor's to buy a new suit. Which afternoon could 
we go together ? 

*io. I don't like sea voyages ; and I don't like 
the seaside. I must spend Easter either in France, 
or among the Scottish Hills, or on the South Coast. 
Which shall it be ? 

1 1 . Ethel has twice as many apples as John : 
Lucy has half as many as John : Lucy has ten. 
How many has Ethel ? 

12. Edith is fairer than Olive, but she is darker 
than Lily. Who is darker — Olive or Lily ? 



BURT'S REASONING TESTS 95 

*I3« The person who stole Brown's purse was 
neither dark, nor tall, nor clean-shaven. The only 
persons in the room at the time were : (1) Jones, 
who is short, dark and clean-shaven. (2) Smith, 
who is fair, short and bearded. (3) Grant, who is 
dark, tall, but not clean-shaven. Who stole Brown's 
purse ? 

Nine Years 

14. C is smaller than B : B is smaller than A. 
Is A greater than C ? 

15. A burglar entered my room at the Hotel 
Splendid last night. The windows were all securely 
fastened on the inside, and the fastenings and the 
window-panes are undisturbed. The opening up 
the chimney is only nine inches square. The door 
opening into the main corridor was locked and the 
key left on the outside. The ceilings, walls and 
floor have no other openings, either secret or forced, 
through which he could have entered. How did 
he get in ? 

*l6. Three boys are sitting in a row : Harry is 
to the left of Willie ; George is to the left of Harry. 
Which boy is in the middle ? 

17. If I have more than a shilling I shall either 
go by taxi or by train : if it rains I shall either go 
by train or by 'bus. It is raining, and I have half a 
crown. How do you think I shall go ? 

18. On one side of my street the houses all have 
odd numbers, beginning with the grocer's, which 
is No. 1. On the other side the numbers are even ; 
No. 2, the baker's, being opposite No. 1. My 
house is No. 16. Walter is my next-door neigh- 
bour : you pass his house as you come up from the 



96 MENTAL TESTS 

baker's just before you get to mine. What is the 
number on his door ? 

*I9« In cold, damp climates, root crops like 
potatoes and turnips grow best ; in temperate climates 
there are abundant pastures, and oats and barley 
flourish ; in sub-tropical climates, wheat, olives 
and vines flourish ; in tropical climates, date palms 
and rice flourish. The ancient Greeks lived largely 
on bread, with oil instead of butter : they had wine 
to drink and raisins for fruit. Which climate do 
you think they had ? 



Ten Years 

20. Some children were asked : " Why are towns 
nearly always more unhealthy than the country ? " 
They gave the following replies : (i) " Some country 
places are by the seaside." (2) " There are more 
doctors in the towns." (3) " The smoke of the 
houses and the breath of the people prevent the 
air from being fresh." (4) " The cottages in the 
country are dark, tiny, and badly built." (5) 
" Disease spreads where people are crowded to- 
gether." Which two children gave the best 
answers ? 

21. " Drinking the sea dry." " Catching the 
wind in a cabbage net." " Gathering grapes from 
thistles." " Washing a blackamoor white." " Touch- 
ing the end of a rainbow." All these sayings mean 

something that is ? (Give the meanings of all 

of them in one word.) 

*22. The doctor thinks Violet has caught some 
illness. If she has a rash, it is probably chicken-pox, 
measles or scarlet fever. If she has been ailing with 



BURT'S REASONING TESTS 97 

a cold or cough she may develop whooping-cough, 
measles or mumps. She has been sneezing and 
coughing for some days, and now spots are appearing 
on her face and arms. What do you think is the 
matter with Violet ? 

23. "I sprang to the stirrup and Joris and he : 

I galloped, Dirck galloped, we galloped 
all three." 

What was the name of the person referred to as 
" he " in these lines of poetry ? 

24. The Duchess of Dustiland's diamonds have 
been stolen. After the ball at the palace she gave 
them to her manservant to take home, with instruc- 
tions to hand them over to her maid at once. When 
he was half-way home he met a friend, and a few 
minutes afterwards a man in blue uniform and helmet 
came up to -them and said : " I arrest you for stealing 
the Duchess of Dustiland's jewels." They were 
taken to a large building outside which a blue lamp 
was hanging with the words " Police Station " 
printed on it. Here another man in uniform took 
possession of the diamonds, and locked up both 
the manservant and his friend in a small, bare room 
for the night. When day dawned, hearing nobody 
about they climbed out through the window, but 
could see nothing of either the lamp or policemen. 
The Duchess is still looking for her jewels. Who do 
you think is the thief ? 

*2$. There are four roads here. I have come 
from the South and want to go to Melton. The 
road to the right leads somewhere else : straight 
ahead it leads only to a farm. In which direction 
is Melton — North, South, East or West ? 



98 MENTAL TESTS 

Eleven Years 

26. A man was found nearly dead with his throat 
cut, and on the back of his left arm there was a 
blood-stained mark of a left hand. The policeman 
says he tried to kill himself. Do you think the 
policeman was right ? 

27. C is West of B : B is West of A. Is A to the 
North, South, East or West of C ? 

*28. Father has just come home in a brand new 
overcoat : there is clay on his boots, and flour on his 
hat. The only places he can have been to are North- 
gate, Southgate, Westgate or the City. He has 
not had time to go to more than one of these. 
There is no clay anywhere in the streets except 
where the pavement is up for repair. There are 
tailor shops only in Southgate, Westgate and the 
City. There are flour mills only in Northgate, 
Westgate and the City. I know the roads are not 
being repaired in the City, though they may be in 
the other places. Where has father been ? 

29. The following are some of the occasions on 
which people shed tears : People laugh till they 
cry. When they are very unhappy they weep. 
A fly in the eye makes the tears flow. Peeling 
onions, scraping horseradish, going through smoke, 
a cold wind in the face — all make the eyes water. 
These instances suggest two general causes which 
produce tears. What are they ? Choose your 
answer from the following phrases : (1) Moderate 
happiness. (2) Bright colours such as red and green. 
(3) Germs. (4) Violent emotions. (5) Irritation of 
the eye-ball. (6) A warm temperature. 

30. In our school a third of the school play 



BURT'S REASONING TESTS 99 

football, and a third play cricket. (1) Are there 
any who play neither football nor cricket ? (2) Are 
there any who play both ? (If it is impossible to 
tell without asking further, say so.) 

*3I. Where the climate is hot, aloes and rubber 
will grow : heather and grass will only grow where 
it is cold. Heather and rubber require plenty of 
moisture : grass and aloes will grow only in fairly 
dry regions. Near the river Amazon it is very hot 
and very damp. Which of the above grows there ? 

Twelve Years 

32. My brother writes : " I have walked over 
from Byford Wood to-day, where I had the mis- 
fortune yesterday to break a limb." Can you guess 
from this which he probably broke — his right arm, 
left arm, right leg, or left leg ? 

33. In the old world the most thickly-populated 
parts have usually been India, China, and the South 
and West of Europe. In India and China the 
rainfall is high in the summer ; on the shores of the 
Mediterranean it is high during the winter ; on the 
shores of the Atlantic it is fairly high all the year 
round. In the deserts of Russia, Persia and Africa, 
it is dry all the year round. Africa is very hot ; 
India and China are very warm ; South and West 
Europe rather warm ; the deserts of Russia cold. 
What kind of climate seems to have helped the 
growth of civilisation most of all — cold and dry, 
warm and dry, or hot and dry ? cold and wet, warm 
and wet, or hot and wet ? 

*34_. Field-mice devour the honey stored by the 
humble-bees : the honey which they store is the 



ioo MENTAL TESTS 

chief food of the humble-bees. Near towns there 
are far more cats than in the open country. Cats 
kill all kinds of mice. Where, then, do you think 
there are most humble-bees — near towns or in the 
open country ? 

35. My birthday is on December 27, and I am 
just four days older than Tom. This year Christmas 
Day comes on a Tuesday. On what day of the 
week is Tom's birthday ? 

36. If the train is late he will miss his appoint- 
ment : if the train is not late he will miss the train. 
We do not know whether the train was late or not. 
Can we tell whether he kept his appointment ? 

*37. I started from the church and walked 100 
yards ; I turned to the right and walked 50 yards ; 
I turned to the right again and walked 100 yards. 
How far am I from the church ? 

Thirteen Years 

38. Explain how the following code is worked : 
Message (in code) . dpnf up Mpoepo bu podf. 
The same (translated) come to London at once. 

What is the secret letter for " x " in this code ? 

39. Dismal Johnny said to Sunny Jim : "If I 
marry I shall be miserable, because I shall be bothered 
with looking after my wife ; if I don't marry I shall 
still be miserable, because I shall have no wife to 
look after me. So in either case I shall be miser- 
able." Sunny Jim replied : " On the contrary, you 
ought to be happy in either case ; for, if you do not 
marry, you will be happy, because you will not be 

bothered with looking after your wife, and " 

How do you think he finished his argument ? 



BURT'S REASONING TESTS 101 

*40. A pound of meat should roast for half-an- 
hour ; two pounds of meat should roast for three- 
quarters of an hour ; three pounds of meat should 
roast for one hour ; eight pounds of meat should 
roast for two hours and a quarter ; nine pounds of 
meat should roast for two hours and a half. From 
this can you discover a simple rule by which you 
can tell from the weight of a joint how long it 
should roast ? 

41 . I walked 10 yards down High Street ; I turned 
to the left and walked 15 yards down Thomas 
Street ; I turned to the left again and walked 10 
yards down James Street ; I turned to the left 
again and walked 15 yards down another street; 
I turned to the left again and walked 10 yards down 
that street ; I turned to the left again and walked 
5 yards. What street was I in ? 

42. 1 is 1, that is, 1 times 1. 

1 and 3 added together are 4, that is, 2 times 2. 
1 and 3 and 5 added together are 9, that is, 

3 times 3. 
1 and 3 and 5 and 7 added together are 16, 

that is, ? 

Look at the above carefully. Can you see a simple 
rule for guessing the answers without adding up the 
figures ? Work the following sums yourself ; this 
will help you to find the rule : (i) 1 and 3 and 5 and 

7 and 9 added together are , because this is 

times . (ii) What do the first seven odd 

numbers (1, 3, 5, 7, 9, 11, 13) come to when added 

together ? This is times . Use the rule 

to find how much the first hundred odd numbers 
would come to if added up. 



102 MENTAL TESTS 

*43. What conclusions can you draw from the 
following facts ? Iron nails will not float in a pool ; 
a cup of pure gold dust weighs nearly twenty times 
as much as a cup of water of the same size ; if you 
drop a silver sixpence or a copper coin into a puddle, 
it will sink to the bottom ; a cubic inch (about a 
tablespoonful) of water weighs less than half an 
ounce ; a cubic inch of brass weighs over two 
ounces ; a leaden weight will drop to the bottom 
of the ocean. Sum up all these observations in one 

short sentence of the following form : " Most 

are ." 

Fourteen Years 

44. When you enter my house you will find a 
window on your right in the side wall of the passage. 
When the sun sets it shines straight through this 
window on to the wall opposite. What direction 
are you facing when you stand in the doorway and 
look across the street ? 

45. If the A's have a bigger army than the B's 
we ought first either to fight the B's, or attack the 
C's by sea, but not attack the A's ; if their army 
is smaller we should attack the A's first. If the C's 
have a bigger navy than we, we ought to fight either 
the B's or the A's, but not the C's. If their navy 
is smaller, we should first attack the C's by sea. 
The size of their armies and navies is as follows — 



A. 


Men 
7,000,000 


Ships 
300 


B. 
C. 

Ourselves. 


5,000,000 
4,000,000 
6,000,000 


400 
500 
200 



Whom should we attack first ? 



BURT'S REASONING TESTS 103 

*/\6. John said : " I heard my clock strike yester- 
day ten minutes before the first gun fired. I did 
not count the strokes, but I am sure it struck more 
than once, and I think it struck an odd number." 
John was out all the morning, and his clock stopped 
at five to five the same afternoon. When do you 
think the first gun fired ? 

47. Mary has just taken a penny ticket. The 
trains from this station all stop at Euston, but after 
that some go to Chalk Farm and Golders Green ; 
others go to Kentish Town and Highgate. They 
stop nowhere else. The fare to Euston, Chalk 
Farm or Kentish Town is a penny : to Highgate or 
Golders Green twopence. Mary did not get in 
the Golders Green train. To what station do you 
think she is travelling ? 

48. They say that in Dodoland hundreds of years 
ago all the kingfishers had legs about six inches 
long, and beaks about two inches long, and they 
used to wade in the water to catch fish for food. 
The individual birds might differ from one another 
in the length of their beaks and legs by about half 
an inch or so—- not more. But the offspring of the 
birds with the shortest legs or beaks would inherit 
legs and beaks equally short, though again the 
brothers would differ a little from each other ; and 
similarly with the birds whose parents had longer 
legs and longer beaks. And the same happened 
with each succeeding generation. Now in those 
days the pools were only four inches deep. But 
they got gradually deeper and deeper ; and to-day, 
where the fish swim, the water is always a foot 
deep at the very least. Kingfishers of the ancient 
kind would now-a-days either drown in the deep 



104 MENTAL TESTS 

water, or starve for lack of food ; for they could 
never learn to swim. What, then, do you think 
has happened to these wading birds in the course 
of centuries ? 

*49« Captain Watts and his son James have been 
found shot — the father in the chest, and the son in 
the back. Both clearly died instantaneously. A 
gun fired close to the person — as, for example, 
when a man shoots himself — will blacken and even 
burn the skin or clothes ; fired from a greater 
distance it will leave no such mark. The two 
bodies were found near the middle of a large hall 
used as a rifle range. Its floor is covered with 
damp sand, which shows every footprint distinctly. 
Inside the room there are two pairs of footprints 
only. A third man standing just outside the door 
or window could aim at any part of the room, but 
the pavement outside would show no footmarks. 
Under Captain Watts's body was found a gun ; 
no such weapon was found near James. In each 
case the coat, where the bullet entered, was blackened 
with gunpowder, and the cloth a little singed. 
Captain Watts was devoted to his son, and would 
have died sooner than harm him purposely ; hence 
it is impossible to suppose that he killed him deliber- 
ately, even in self-defence. But some think that 
James secretly disliked his father, and hoped to inherit 
his fortune at his death, (i) Was Captain Watts's 
death due to murder, accident or suicide ? (-2) 
Was James's death due to murder, accident or 
suicide ? 

50. The crust of the earth — that is, the outer 
layer down to at least fifty miles below the top — 
consists chiefly of rock and stone. Rock and stone 



BURT'S REASONING TESTS 105 

weigh about three times as much as a bulk of water 
of the same size. The heaviest materials found in 
the crust of the earth are metals ; but in the outer 
layer of the earth these are, of course, comparatively 
rare. The earth as a whole weighs over five times as 
heavy as a globe of water of the same size. What 
does this suggest that the interior and middle of 
the earth are mainly composed of — water, rock and 
stone, metal or hot gas ? 



CHAPTER VI 

THE MEASUREMENT OF KNOWLEDGE 

The heart of the problem may best be made 
manifest to the reader by supposing that a father 
brings to him a boy of ten years of age with the 
request that he should ascertain whether that boy, 
who is, say, attending a dame's school, is up to the 
average in his school studies. The father does not 
want to know anything about the boy's intelligence 
(no father ever doubts that), but he does want to 
know whether the school is giving him value for 
his money — a matter which all parents frequently 
call into question. Have we any means of telling 
with any degree of exactness whether the lad is of 
average proficiency in such rudimentary branches of 
instruction as reading, composition and arithmetic ? 
Until quite recently we had not. We did not know 
what the average child of that age could perform : 
the most we could do was to make a rough guess ; 
and the value of that guess depended purely upon 
personal judgment, which again depended upon the 
range and nature of personal experience. We had, 
in fact, no stable standards of measurement. Each 
man measured for himself, and each measured with 
a private yard-stick. And even to-day the position 
is not much better. We have only just begun to 
standardise our tests, and have merely arrived at a 

106 



MEASUREMENT OF KNOWLEDGE 107 

few tentative standards of achievement in the 
simplest of processes. There is an urgent call for 
the extension of this work. 

Many are the motives that urge us to make the 
attempt. In France the aim has been to find the 
child who fails to benefit by the ordinary instruc- 
tion of the e coles primaires. Binet's motive in for- 
mulating his Bareme d 'Instruction was the same as 
his motive in establishing his scale of intelligence — 
the quest of the subnormal child. But other motives 
are constantly operative. There is a need for stan- 
dards of comparison between the achievements of 
children of different races, of different historic 
periods, of different environments, and under 
different types and modes of education. Pedagogic 
records are no less useful than athletic records. It 
is surely as profitable to know how long it would 
take a nine-year-old child to add a given column 
of figures as it is to know how long it would take 
a two-year-old horse to run a mile. Yet we have 
records in the one case and not in the other. 
Finally, there is the need for placing in the hands 
of the class teacher some means of protection against 
arbitrary and unreasonable criticism by the head- 
master or the inspector. 

It is well to be quite clear as to the precise 
nature of the standards we wish to establish ; for 
there are three distinct possibilities. We may ascer- 
tain what children of a given age actually do do, 
or what they can do, or what they ought to do. 
The first standard is actual, the second maximal, 
and the third ideal. And none of them can be 
either deduced from a priori principles or extracted 
from the inner consciousness of a Board of Examiners. 



108 MENTAL TESTS 

Our scale must rest on measurable facts, must be 
built up by a careful investigation into the actual 
achievement of children under clearly defined con- 
ditions. What standard of proficiency in reading, 
for instance, or in spelling, or in arithmetic, can be 
expected of London children of a given age under 
their present conditions of schooling ? The simplest 
and most convenient means of ascertaining this is 
to devise a suitable test (by no means an easy 
matter), apply it to as large a number of children 
as possible, and submit the results to statistical 
analysis. The scale thus arrived at will afford what 
may be called, by way of distinguishing it from the 
other two types of standard, Norms of Performance. 
These norms have a simple and definite meaning ; 
they can be verified or modified by further testing, 
and they have a definite range of usefulness. 

Is it possible to establish either of the other two 
standards ? And if possible, is it expedient ? Is 
there any point, for instance, in trying to discover 
what the result in arithmetic would be if all the 
schools in London were to sacrifice for a time every 
kind of intellectual activity in order to secure 
maximal proficiency in this one direction ? There 
evidently is not. Apart from the violence done to 
the victims of the experiment, the results would 
be of no value. Can we deduce from the norms 
of actual performance some sort of ideal standard 
which would serve as an index of what the children 
ought to do as distinct from what they do ? I 
myself see no scientific way of doing so. Where 
ethics and aesthetics have failed, it does not seem 
likely that pedagogics will succeed. We have there- 
fore to fall back on norms of actual performance as 



MEASUREMENT OF KNOWLEDGE 109 

constituting the only type of standard which proves 
to be both practicable and useful. Of the other 
two, one is practicable without being useful, and 
the other useful without being practicable. 

Let us now consider what attempts have actually 
been made to arrive at standards or norms of 
instruction. They first appear in the guise of 
curricula issued by a central authority. In our own 
country the Board of Education's standards of 
examination are familiar to all those who remember 
the days of payment by results. Indeed, they have 
not yet quite disappeared from the Code of Regula- 
tions : they appear in a modified form in the section 
on certificates of proficiency. It may be said at 
once that they do not represent any pure type of 
standard, as the word is used in this book. They 
are neither actual, maximal, nor ideal. Partaking 
of some of the worst features of each, they are 
hybrids of very doubtful pedigree. Based originally 
on the opinion of what certain authorities at the 
Education Department thought reasonable, moulded 
to suit the exigencies of examination, they lacked a 
solid foundation of objective fact. Moreover, the 
scheme was used, and, indeed, intended to be used, 
in such a way as to exemplify what Professor Adams 
has pointed out to be the one great danger to which 
all norms or standards are exposed : it was used as 
a goal, and not merely as a test. Since preparation 
for annual examinations was at that time virtually 
the sole aim and purpose of the school, it was 
inevitable that these standards of examination 
should become syllabuses of work ; should form the 
ground of the classification of scholars ; should, by 
simple metonymy, give their name to the classes 



no MENTAL TESTS 

preparing for the specific examinations ; and, finally, 
be regarded as norms of performance for children 
of various ages. Thus the word tried to do several 
distinct pieces of work, and did none of them well. 

As examination syllabuses and schemes of study, 
the standards were marred by serious faults. In 
the first place, they were often so vague as to be 
almost useless. The reading requirement for Stan- 
dard III, for example, was " To read a passage from 
a reading-book " ; and for Standard IV, " To read 
a passage from a reading-book or history of England." 
Neither sentence tells us more than the first two 
words alone. No indication is given of the mode 
of judging whether a child has reached the specified 
standard, nor any indication as to the amount of 
progress in reading to be expected of a child between 
the ages of ten and eleven, the normal ages for 
" passing " these standards. Secondly, the scale 
involved too high a standard of mechanical accuracy 
— a standard which could not be reached without 
an undue expenditure of time, and a consequent 
narrowing of the curriculum and loss of interest. 
With the present wide and generous scheme of 
studies, so high a level of attainment in one direction 
would be difficult, if not impossible. Finally, as 
norms of achievement, the standards of examination 
were woefully defective. Even supposing that some 
objective means of testing were prescribed, so that 
two independent examiners would inevitably arrive 
at the same results (which was certainly not 'the 
case), the standards themselves were arbitrary and 
lacked the guarantee of a careful scientific study of 
the normal capacities of children. 

Nor did the schedule of standards represent a 



MEASUREMENT OF KNOWLEDGE in 

real age scale. Although a normal pupil was sup- 
posed to pass through each of the seven standards 
before he reached fourteen years of age, he could 
only pass one a year ; and while a stroke of bad 
luck would put him back a whole year, no amount 
of good luck could put him forward a day. The 
consequence was that retardates were plentiful and 
accelerates entirely absent. 

A very different kind of standardisation is that 
of Binet. His Bar erne & Instruction was based on 
the mean performance of a large number of Parisian 
children. It supplies, in fact, real norms in three 
important branches of instruction — reading, number 
and spelling. But although the aim is laudable, the 
table published in Les idees modernes sur les Enfants 
is of no great value. As the term " Bareme " 
implies, it claims to be a ready reckoner — a rough- 
and-ready means of finding out whether a child of 
a given age has profited adequately by his schooling. 
But its very roughness and readiness constitute its 
main defect. It is supposed to take only ten minutes 
to assess a child's scholarship — to fix his position in 
the age scale ; and it is hard to believe that so 
meagre and hurried an examination can gauge the 
effect of years of teaching. 

Binet's method of judging the reading is based 
on the position of the pauses made by the reader. 
If he pauses between the syllables, it is marked 
" syllabic " ; if he pauses between the words, it is 
marked " hesitant " ; and if he does not pause at 
all, except where the sense of the passage demands 
it, the reading is marked " current." In all, five 
grades of proficiency are indicated — subsyllabic, 
syllabic, hesitant, current and expressive. This 



ii2 MENTAL TESTS 

seems a simple scheme, and if it were easy to apply, 
its obvious lack of delicacy of gradation might be 
overlooked. But, as a matter of fact, it is impos- 
sible to apply it with any feeling of certainty. It 
is very rare that any child's reading is found to fall 
entirely within any one of the prescribed grades. 

In arithmetic simplification is again aimed at. 
Binet goes so far as to contend that it is unnecessary 
to test both addition and subtraction, for a know- 
ledge of the latter implies a knowledge of the former. 
By parity of reasoning, a test in division is claimed 
to render a test in multiplication unnecessary. 
Indeed, three simple questions for each child seem 
to be considered adequate ; but each question must 
be given in concrete form. To illustrate the kind 
of question he advocates, I will cite his typical 
example for children between six and seven years 
of age : " From 19 apples take away 6 apples : 
how many remain ? " 

The spelling test is of no value outside France ; 
for it is a test of grammar as well as of spelling — 
the two being inseparable in the French language. 
This peculiarity is rendered obvious by the typical 
sentence given in the Bareme : " Les jolies petites 
filles etudient les plantes qu'elles on remasses hier " 
— a sentence abounding in pitfalls. 

Turning from France to America, we find there 
the home of standardisation. A tremendous volume 
of work has been done by Thorndike, Courtis, Ayres, 
Terman, Munroe, Judd and others with a view to 
reaching as much exactitude as the nature of the 
subject will permit. But its usefulness for us is 
marred by its insularity — by the fact that it is 
American and not English. Their arithmetic tests 



MEASUREMENT OF KNOWLEDGE 113 

abound in dollars and cents, their problems often 
refer to customs and transactions peculiar to them- 
selves, and the spelling is Websterian. The next 
serious defect, however, is that the results are not 
embodied in an age scale, but in a grade scale. We 
are told what level the children in Grade IV, say, 
of a certain American school, did, on an average, 
attain in arithmetic, spelling and reading. But we 
are not told the actual age of these children. Nor 
can we infer it from the grade. We learn from 
their educational papers that the ages in the grades 
are not what they are theoretically supposed to be. 
They vary from school to school, and from city to 
city. Moreover, it makes a very great difference 
whether the tests were given at the beginning, the 
middle, or the end of the school year. Binet's 
scales are of universal value because they are age 
scales ; and if the American scales are to be used 
in England they must be translated from grade 
scales to age scales. They will then cease to be 
national and become international. 

I must emphasise the fact that the tests are 
merely tests, and that their value diminishes in the 
proportion that they deflect the general course of 
study. Although in those rudimentary habits which 
are the beginnings of school pursuits this danger 
may be met by making the tests comprehensive, 
that device is impossible in those higher and more 
advanced branches of study where no test can cover 
more than a small fraction of the whole field. We 
have, in fact, ultimately to rely on the co-operation 
and good faith of the teacher. And my experience 
goes to show that such confidence is rarely misplaced. 

It has been urged as an objection to the use of norms 
1 



ii4 MENTAL TESTS 

that they refer to the most measurable school sub- 
jects, and the most measurable are the least valuable. 
There is thus a danger that the teacher will con- 
centrate his efforts on the more mechanical aspects 
of school work, to the neglect of the higher and 
more spiritual aspects. As a matter of fact, this 
fear is groundless. Norms in the mechanical sub- 
jects are just as much a protection as a menace. 
They will probably show that in some schools the 
mechanical work is too good : it is so far above the 
normal that too much time and attention have been 
devoted to it. When the norm is reached further 
" drill " is for the time unnecessary. The teacher 
would realise that he could with a clear conscience 
reduce the drudgery and render the work more 
recreational and more broadly cultural. What is 
really aimed at in establishing the more mechanical 
norms is the discovery of that degree of automatism 
which best serves the interests of the higher pro- 
cesses of thought. And in any given school it may 
be just as necessary to slacken the standard as to 
string it up. 



CHAPTER VII 

DISTRIBUTION AND DISPERSION 1 

When we measure a multitude of natural objects 
belonging to the same genus or class we find that 
the results tend to assume a determinate shape. 
The magnitudes occur in accordance with a general 
law. Let us suppose, for instance, that we start 
measuring the heights of adult Englishmen by 
making one after the other stand against a post and 
marking each height with a horizontal stroke. If 
we choose our specimens at random we shall soon 
find our marks tending to crowd round a fixed 
height. By the time we had measured ioo the 
marks would appear somewhat as in Fig. I. The 
largest number of marks would probably fall between 
6j and 68 inches, and the numbers would tail off 
as they diverged in either direction from this central 
position. As the number of men increased we should 
find our range of heights extending, for we are 
much more likely to find a giant or a dwarf among 
10,000 men than among fifty. By the time 8000 
had been measured we should probably find our 
range extending from 57 to 78 inches. Let us now 

1 For a fuller treatment of this subject the reader is referred 
to Nunn's Exercises in Algebra, Vol. II. , Sec. IX. (Longmans). 

Some excellent diagrams illustrating distribution and dispersion 
will be found in Burt's Educational Abilities (King and Son). 

i J 5 



n6 



MENTAL TESTS 



take our ioo men, or, for statistical convenience, 
let us say ninety-nine, and put them to stand in a 
row in order of height so that the tallest stand at 
one end of the row and the shortest at the other. 
An unreflecting observer would expect the line 
joining the tops of their heads to be a straight line. 



Figs. land 2. Probable heights of 99 
Englishmen- taken at 



Quartile. 



Inches 


7+1 




7 3 " 




7* 


— 


V 

70- 


n 


69- 


- : 5^ UblwT 


66- 

6 7 - 


^ — Nedian 


66- 


^52— Latter 
=f Qvartik 


65- 


s 


64- 


= 


63 


~ 


61 


t 


6m 


E 


6o- 

59 


1 


5$\ 






f'a 



99»ien standing in a row in. oraitr of height (£ou«si s6"tnniiu<l) 

Ka.x 



In fact, however, the line tends to take the forms 
of an Ogive — the curve represented by Fig. 2. 
This, indeed, could be deduced from the facts 
recorded in Fig. 1. Let us arrange the results in 
yet another way. If we erect a column, A (Fig. 3), 
proportional to the number of measures that fall 
between 6j and 68 inches, place to the right another 
column, B, proportional to the number of measures 



DISTRIBUTION AND DISPERSION 117 

that fall between 68 and 69, and so on for the 
other groups of measures, we shall get what is 
called a frequency-column-graph, or a surface of 
frequencies. 

It is clear that we have not been dealing with 
discrete units like the abstract numbers 1, 2, 3, 4, 
etc., but with continuous magnitudes. For there 
is no limit, except those imposed by our instru- 
ments and our sense-organs, to the number of 



ZZ3 



Inches 6/ Sz 65 6<J- 65 66 6f 6% 69 70 7/ ~]2- 73 74- 

f^.3 frecucncy-ccJumn.- graph- . 

different measurements that may be made between, 
say, 6y and 68 inches. Nor is there any fixity 
about the group-range. We have chosen one inch, 
but we might just as well have chosen half an inch, 
or a quarter of an inch, or, indeed, any range we 
liked. It is obvious, however, that the smaller the 
range of statures the smaller the number of men 
whose statures fall within that range ; and to show 
the general scheme of distribution it is most con- 
venient to choose one's range in accordance with 



n8 



MENTAL TESTS 



the number of men measured. If the numbers are 
very large we can conveniently make our columns 
thinner ; and by increasing the numbers and 
diminishing the range we find the zigzag formed 
by the tops of the columns tending towards a 
continuous curve, as in Fig. 4. This peculiar bell- 
shaped curve is known as a frequency curve. The 
particular type here illustrated, to which stature 
closely conforms, is called the Curve of Normal 
Distribution. 



, > * — j — 1 



Jnrfrraijmttl 



TOTjige 



i- fle a n 



Variation | 
" Dtytatioh.' 



65 64. 6S 66 6J 68 69 70 7/ 

%4-. Gitvs ofriormal dlslnhut 



71 73 7+ 75- 76 



ion. 



If instead of taking the men's heights we had 
taken their weights, we should have found the 
measurements distributed in almost the same way. 

Finally, when instead of a physical trait we 
measure a mental trait we appear usually to get the 
same type of result. A number of girls, say, of 
eleven years of age exhibit degrees of educational 
ability which, when carefully tested, prove to be 
distributed in much the same way as their heights 
or weights. In other words, examination marks 



DISTRIBUTION AND DISPERSION 119 

should follow the same law as the measurements 
of other natural features : they should roughly 
conform to the Curve of Normal Distribution. 

This curve is also called the Curve of Probability 
and the Curve of Error. The term Curve of Prob- 
ability derives from the fact that the curve shows 
the frequency of a series of events composed of a 
number of factors when the presence or absence of 
a given factor is determined merely by chance. 
Suppose, for example, I have two coins, toss them 
up again and again, and make a record of the 
number of times there is no head, the number of 
times there is only one head, and the number 
of times there are two heads. I shall find the 
score for the three cases tending towards the pro- 
portion of 1, 2 and 1. This, indeed, could be 
deduced by the laws of probability from the fact 
that there are but four possible ways in which the 
coins can fall, viz. TT, TH, HT and HH ; and 
out of these four " no head " appears once, one 
head twice, and two heads once. If instead of the 
presence of heads we had considered the absence 
of heads, or the presence or absence of tails, we 
should have got the same result. The same kind 
of thing, too, will happen if we toss three coins a 
large number of times, except that the proportion 
would now be that of 1, 3, 3 and 1. The case of 
no head (or three tails) would occur about once 
every eight throws, one head about three times, 
two heads about three times, and three heads about 
once. With four coins the probable ratios would 
be 1, 4, 6, 4 and 1. The reader will by this time 
have observed that the proportions I have given 
are the coefficients of the expansion of (x + i) 2 , 



i2o MENTAL TESTS 



(x + i) 3 and (x + i) 4 ; and if he will proceed to 
expand the higher powers of the binomial and 
represent them by frequency-column-graphs, he 
will find that the graphs gradually approximate the 
curve in Fig. 4 — the curve of probability. 

The term Curve of Error is a relic of an older 
nomenclature. The curve was, in fact, first studied 
in connection with errors of observation, particu- 
larly in astronomy ; and a tendency arose to call 
all divergences from a mean " errors." In gunnery, 
too, it was natural to regard as errors all the shots 
that missed the mark. 

It should be strongly emphasised that the curve 
is an ideal curve. It is seldom or never actually 
reached : it merely marks a limit towards which 
the values tend — an ideal arrangement to which 
they approximate more and more as certain con- 
ditions (those of pure chance) are fulfilled. Infer- 
ences drawn from it, arguments based on it, are 
never certain : they are only probable. For it is 
the main characteristic of all inferences from statis- 
tical uniformities, that as they increase in particu- 
larity they diminish in certainty. They are whole- 
sale truths, not retail truths. The smaller the 
number of cases the less sure we feel that any 
general statement will hold good. But the number 
of children grouped in a class is rarely so small 
that a central tendency is not observable ; and if 
the results of examining them depart widely from 
the normal type, it shows that the examination was 
unsuitable. It was either a bad examination, or a 
bad sample of children — bad in the sense of not 
being representative. A picked sample, it is true, 
always exhibits certain peculiarities ; but these. 



DISTRIBUTION AND DISPERSION 121 

should be allowed for : they should not come as a 
surprise to the examiner. The results of an 
examination are, in fact, a standing criticism of the 
examination : they search the suitability of the 
questions and the correctness of the marking. 

From what we have already said certain important 
principles may be deduced — 

(1) On an ideal examination mark-sheet, where 
the candidates have been ranked in order of merit, 
the degrees of difference between consecutive marks 
are not equal. They are greatest at the extremes, 
and gradually diminish as they approach the middle. 

(2) If equal ranges of ability be taken, the number 
of cases falling within the central range is large, and 
the number within the extreme ranges small. If, 
therefore, we arrange the examinees in three groups, 
A, B and C, representing equal ranges of ability, 
the B group should be the largest, and the A and C 
groups should be about the same size. Similarly, 
if we classify them in five groups, A, B, C, D and E, 
the C should be the largest group, the B and D 
the next, and the A and E the smallest. 

(3) A series of tests of any mental quality or 
attainment should be so devised, and the results so 
marked, that nobody should gain full marks, nobody 
gain none, and the average gain about half marks. 
This is an ideal examination which is never in 
practice attained. When the aim of the examina- 
tion is to pick out the brightest intellects these 
conditions do not hold good. 

(4) The range of marks between the median, or 
middle mark, and the quartile (the mark half-way 
between the middle and the ends) is less than that 
between the quartile and the extreme, 



122 



MENTAL TESTS 



It must not be thought that every test the 
teacher sets his class can give results which accord 
with these rules. It may be, for instance, that the 
test is only intended to divide the class into passes 
and failures, to find out those who can do a certain 
simple thing and those who cannot. This sheep-and- 
goat classification is extremely useful for teaching pur- 
poses, and may involve any degree of inequality in 
the sizes of the two groups. 




Marks IS 



10 IS 3C 35 40 ^5 SO SS <SO 65 JO JS SO 65 

5 SteuuCuTve 



% 



Nor must it be assumed that the series is always 
symmetrical. In fact, the curve is as often as not 
skewed, as in Fig. 5 : the numbers crowd towards 
the right or towards the left. There is a general 
rise and a general fall, but one is often steeper than 
the other. 

The only way to describe "a series of measure- 
ments fully is to state all the facts, either by giving 
the actual measurements or by representing them 
by a graph. But we rarely use all these facts : we 
are generally content to know their central ten- 
dency, and to take that value as representative of 



DISTRIBUTION AND DISPERSION 123 

the whole series. When the series is normally dis- 
tributed the central tendency is represented by the 
average or arithmetical mean. If the terms of this 
normally distributed series be arranged in order of 
magnitude the mean is also the median or middle 
term. But when the series is not symmetrical the 
mean is not in the middle, and its right to repre- 
sent the series has been disputed. It is claimed 
that the median represents it better. Take, for 
example, the series (a) 1, 2, 3, 3, 3, 4, 19. The 
average here is 5, but it is clear that the median, 3, 
is a better index of the central tendency than 5. 
It may, in fact, be stated generally that when 
erratic items disturb the tenor of the series, the 
median is better than the mean as a measure of 
the central tendency. But there are, on the other 
hand, other abnormal occasions when the average 
is the better measure. Take, for instance, the 
series (b) o, 1, 1, 7, 7, 8, 11. The median, 7, is 
clearly too high. The average, 5, is better. And 
in the series (c) o, o, o, 8, 9, the median, o, would 
be entirely misleading. 

It is sometimes suggested that the mode — the 
most frequent value (e. g. 3 in series (a), and o in 
series (c)) — be taken as the representative value. 
But in some series no value occurs more than once ; 
in others it is impossible to decide between rival 
claims (the 1 and the 7, for instance, occur with 
equal frequency in series (b)) ; in others, again, the 
mode occurs at the beginning or end of the series, 
as in series (c), and is a bad representative. 

It may be argued that the series of marks we 
have been citing violate the very rules we have 
already laid down : they depart widely from the 



124 MENTAL TESTS 

normal, and indicate either very bad testing or very 
bad sampling. The charge of bad sampling may 
be admitted, for the class teacher cannot always 
pick his samples : he has to test what children he 
has. Moreover, he has to measure the success of 
his teaching — to find out the extent to which he 
has imparted knowledge or fostered understanding ; 
and here irregular results may reasonably be 
expected, especially if the numbers are small. I 
admit, therefore, that for the purposes of emphasis 
I have taken extreme cases — possible cases rather 
than probable cases. But these infrequent cases 
illustrate conditions which are by no means infre- 
quent. They magnify peculiarities that are nearly 
always present. 

When the series is of normal distribution, it does 
not matter whether we take the mean, the median 
or the mode ; for they all three coincide. When, 
however, the distribution is not normal we have to 
choose between them. The mode we may dismiss 
at once as never quite suitable, and often quite 
inapplicable. Of the other two sometimes one is 
more suitable, sometimes the other ; and rarely is 
either a really bad representative value. For sim- 
plicity of calculation the median is undoubtedly the 
better. 

When we have learnt the average or central ten- 
dency of a series we have learnt the most significant 
thing about it. But there are other things we want 
to know ; and the most important of these other 
things is the degree of scatter — the closenes's or 
looseness with which the various values cluster round 
the average. In series (d) 4, 5, 5, 6, 6, 6, 7, 7, 8, 
for instance, there is very little scatter ; no value 



DISTRIBUTION AND DISPERSION 125 

deviates from either the mean or the median by- 
more than 2. But in the series (e) 1, I, 2, 3, 3, 5, 
8, 14, 17, which has the same average as {d), the 
deviations are very much greater. To evaluate these 
deviations the obvious plan is to treat them as we 
treat the original series, that is, find their average. 
In series (d) the deviations are respectively 2, 1, 1, 
o, o, o, 1, 1, 2, and their average is *8. This is their 
mean deviation from the mean, or, more briefly, their 
mean deviation or mean variation. The mean devia- 
tion of series (e) is 4*6, that is, more than five times 
as great as that of the first series. 

In the same way we can calculate the mean 
deviation from the median, another index of dis- 
persion. 

The simplest and quickest way, however, to 
measure the general degree of deviation is to extend 
the principle of the median, and after finding the 
median, which divides the series into halves, to find 
the median of each of the halves. In other words, 
we arrange the series in order of magnitude, and 
divide it into four equal parts. The value one 
quarter of the .way up is the lower quartile, the 
value half the way up is the median, and the value 
three-quarters of the way up is the upper quartile. 
The difference in value between the upper and 
lower quartile is known as the interquartile range. 
Since this range is an index of dispersion both 
above and below the median, it is usual to halve 
it, and thus get the semi-interquartile range, or 
quartile deviation. This is, in fact, a convenient 
way of averaging the deviations of the two quartiles 
from the median. In the series (J) 1, 2, 3, 3, 4, 4, 
5, 5, 6, 6, 7, 8, 8, 9, 10, for instance, 3 is the lower 



126 MENTAL TESTS 

quartile, 5 the median, 8 the upper quartile, 5 the 
interquartile range, and 2\ the quartile deviation. 
Sometimes the lower quartile is called the 25 per- 
centile, the median the 50 percentile, and the upper 
quartile the 75 percentile. The semi-interquartile 
range is practically the same as the -probable error. 
It is so-called on what seems to be a lucus a non 
lucendo principle ; for it is neither an error, nor is 
it probable. Error means deviation, as in the phrase 
" curve of error " ; and it is only a probable devia- 
tion in the sense that since twice its amount includes 
half the number of values, any particular value is 
just as likely to fall without that amount as within it. 
We have one other means of measuring the degree 
of variation from the central tendency — standard 
deviation, or root-mean-square-deviation. Instead 
of taking the mean of the individual variations from 
the mean, we take the mean of their squares and 
then find its square root. This takes a longer time 
to calculate than any of the others, but it has 
certain advantages. In calculating it we have not 
to commit the algebraical solecism of adding terms 
of opposite signs as if they were signless, as in 
estimating the other measures of deviation ; for the 
squares of all numbers are necessarily positive. 
Moreover, by squaring, extreme deviations are mag- 
nified, and given their due weight as indications of 
individual ability. The very items that cause us 
trouble when we try to find the central tendency 
are of supreme service in calculating the correlation 
of abilities. The best-known method of finding the 
correlation coefficient involves the finding of the 
standard deviation. Those, therefore, who wish to 
make further calculations from an array of values 



DISTRIBUTION AND DISPERSION 127 

are prone to use the standard deviation as a measure 
of variation instead of the simpler measures, or of 
the mental age. Mr. Burt does so. He suggests 
that for strictly scientific purposes it should be used 
in the schools as a unit of measurement. 

In a normally distributed series the quartile de- 
viation is less than the mean deviation, and the 
mean deviation less than the standard deviation — 
a fact illustrated graphically in Figs. 4 and 5. 

I have described various means of finding the 
central tendency of a list of examination marks, 
and various means of finding the deviation from 
that central tendency. From among these there is 
in actual use in the schools only one way of record- 
ing the central tendency, and none of recording 
the deviation. The average, or arithmetical mean, 
is the only statistical device in common use. The 
result of a test in arithmetic is supposed to be 
adequately reported and recorded when the average 
number of sums right is given. And as I have 
already shown, the way of the average is quite a 
good way : it is at least as good as any other. But 
it is not enough. Some mode of expressing the 
degree of dispersion is also necessary — the mean 
deviation, for instance. As a matter of simplicity 
in working, however, and completeness of statement, 
I would commend the method of the median and 
quartile deviation. To record a result it is only 
necessary to give five values — the lowest, the lower 
quartile, the median, the upper quartile and the 
highest. This will give more information in a small 
compass than any other method. The mean devia- 
tion affords no clue to the symmetry of the series, 
for it does not differentiate the deviations below 



128 MENTAL TESTS 

the average from the deviations above the average. 
But the quartiles reveal to us at a glance both how 
and how much the several values are dispersed (see 
Fig. 5). In fact, we learn from the five items men- 
tioned above the range of the series, its central 
tendency, its degree of dispersion, and its mode of 
dispersion. 

The teacher unfamiliar with statistical terminol- 
ogy will no doubt consider these distinctions irri- 
tating and useless. Irritating perhaps they are, but 
not useless. For different investigators affect dif- 
ferent systems. Some find it more convenient to 
reject the average and use the median, others cling 
to the older scheme. Those who wish to base 
elaborate calculations on their data prefer to 
measure dispersion by the standard deviation ; 
while those who desire quick practical results prefer 
the simpler measures, the mean variation or the 
quartile deviation. The few explanations I have 
given should enable the reader to adjust his mind 
to these varying usages. 

I will try to illustrate some of the ways in which 
a broad knowledge of the principles of distribution 
may be useful to the teacher. Let us suppose that 
he has to mark forty composition exercises written 
by the boys in his class. It is doubtful whether he 
can arrange them with any degree of confidence 
into more than ten groups. Although a teacher 
sometimes tries to mark on a scale of 1 00, awarding 
one boy, say, 73 marks and another 74, it is idle to 
pretend that he can make such fine discriminations. 
Generally speaking, ten grades are as many as he 
can manage ; and on a ten-grade basis it is clear 
that the forty papers in question cannot all receive 



DISTRIBUTION AND DISPERSION 129 

different marks. To examine his distribution the 
teacher should, after marking, draw up a frequency 
graph as in Figs. 3, 5, 6 and 7. He will then see 
at once whether he has judiciously apportioned his 
scores. If the bulk of the marks are somewhere 
near the middle it is presumptive evidence of careful 
marking. As an example of bad marking I will 
take an instance that occurred some years ago in 
the top standard of an elementary girls' school. At 
the terminal examination the thirty-five girls in the 
class were examined by the head mistress in com- 
position, 20 being the maximum marks allowed. 
Twelve girls got full marks, five got 19, twelve got 
18, and six got 15. If the reader will plot this 
result either as an ogive or as a frequency graph, 
he will note that the principles I have tried to 
expound are flagrantly violated. In point of fact 
the twelve papers that were awarded full marks 
were of very unequal merit, and it is doubtful 
whether the best of them deserved more than 14 
marks out of 20. 

Both composition and reading are quite frequently 
marked in this haphazard fashion. If more than 
one pupil receive full marks it generally means that 
the best of these pupils is getting less than justice. 
Towards the middle of the scale " ties " are in the 
natural order of things, but the further from the 
middle we get the more unlikely is equality to be 
found. A test, therefore, that fails to differentiate, 
and spread out the pupils at the higher and lower 
ends of the list, is either bad in itself or badly 
marked. 

Let us now consider a subject in which it is 
possible to calibrate more finely. Mathematics, for 

K 



130 



MENTAL TESTS 



instance. Here, with a sufficiently searching exami- 
nation, it is quite possible to find ioo distinct grades 
of proficiency. If the base line of a frequency graph 
be spaced out in equal ranges of from o to 5 per cent., 
from 5 to 10 per cent., from 10 to 15 per cent., 
and so forth, and columns raised proportional to 
the number of pupils whose marks fall within these 
ranges, the result will be a graph or curve of which 
Figs. 5 and 6 are possible varieties. The skew shown 
in Fig. 5 may be due to an imperfect grading in 




Ma-rks XO IS 30 3S 4o ^S So SS 60 6S lo IS Co SS 9a 3S 

H^. 6 Curve cuilK tuJo cresls 

the difficulty of the questions, or to some peculiarity 
in the class itself. When there are two distinct 
crests, as in Fig. 6 — and especially if this duality 
reappears in other examinations — it points to a 
serious lack of homogeneity in the class. These are 
really two central tendencies due to the presence 
of two natural groups. We get this kind of curve 
when we plot the heights of a mixed group of men 
and women. One crest will indicate the central 
tendency of the men, and the other the central 
tendency of the women. A double summit that 



DISTRIBUTION AND DISPERSION 131 

sometimes appears in the plotted results of a com- 
petitive examination probably indicates two distinct 
types of candidates — those who work for the exami- 
nation and those who do not. Peculiarities in the 
curve of distribution, although they fall short of 
proof, always suggest points for investigation. 



nJ 



75* 



£20- 



r 



% 7 



Surface of freousncu of marks 
obtained by £40 girls o{ 9-3i -years 
old in }he Tnechqnical Teading test 

. ■ ■ ■ ■,.,> !~l I" ) 

S 10 is 20 is la as <%> *s So is 60 &s -jo js so es m m /» at iu us m 11s is* as iv u* uz> «cr 

/larks 

I would particularly warn the reader not to 
expect a smooth curve from so small a number of 
cases as a single class provides. Rather should he 
expect something like what is seen in Fig. 7, where 
I have plotted some of the results obtained in the 
reading test described in Chapter VIII. Although 
there are 540 cases dealt with, yet there is much 
irregularity in the rise and fall of the frequencies. 
Indeed, so conspicuous is the fall at 90-95, or 
rather the rise at 100-105, tnat an explanation 



132 MENTAL TESTS 

seems to be called for. As, however, these features 
do not reappear in the corresponding frequency 
surface for boys, I conclude that the causes are 
accidental, and not due to any peculiarity in the 
test. 

Another way of using the notion of normal dis- 
tribution in ordinary class work may be indicated. 
Suppose the teacher has to mark forty drawings. 
Their absolute merit is beyond his, or indeed any- 
body's, power to determine : his concern is to 
appraise them relatively to one another. He will 
find it a good plan to spread the drawings out on 
a large table, and proceed thus : If there is one 
copy which is manifestly the best, mark it io ; and 
if there is a copy which is manifestly the worst, 
mark it I. Then look for the second best — there 
may be two or more. Mark each of these 9. Then 
look for the next to the worst, and mark these 2. 
Work thus towards the middle, making the groups 
larger and larger as the middle is approached. 
Here we have a working conception which will be 
found serviceable as a guiding principle, but dan- 
gerous as a hard-and-fast rule. It is, indeed, very 
improbable that a set of papers if rightly marked 
will tamely fall in with a preconceived scheme, for 
each set will have peculiarities of its own which 
must be recognised ; but it is equally improbable 
that the drawings will depart widely from the 
general scheme I have outlined above. In the final 
issue the marks should fit, not the scheme, but the 
papers. 

In Chapters VIII and X, I give two standardised 
tests in reading and seven in arithmetic. The norms 
appended represent the central tendency (the average 



DISTRIBUTION AND DISPERSION 133 

or the median) of the results obtained by applying 
the tests to several thousands of children in a large 
variety of schools. They indicate the normal 
achievement at the exact age mentioned ; and the 
way to use them is simple. If, for instance, a 
teacher gives the silent reading test to his pupils, 
whose average age is ten years three months, he 
should expect an average score of 11 ; for the table 
of norms gives 10 for ten years of age, and 14 for 
eleven years of age, and his boys are a quarter of the 
way between ten and eleven. 

Judging from the score made in certain individual 
schools, the mean variation for the written arith- 
metic tests is on the whole nearly 50 per cent, of 
the average reached. If, for instance, the norm is 
6, the mean variation is nearly 3. It is larger even 
than this for the younger children, but consider- 
ably smaller for the older. It should be borne in 
mind, however, that in collating my results it was 
not children of the same class or grade or standard 
that were grouped together, but children of the 
same age. And unless the degree of dispersion in 
the class is less than the degree of dispersion in the 
age group, the school is no better organised (for that 
particular subject at least) than if the classification 
of scholars were based strictly upon age. The smaller 
the mean deviation the more homogeneous is the 
class. 



CHAPTER VIII 

READING 

A. — As a Mechanical Art 

What is the fundamental and essential factoi 
in the ability to read ? Binet seems to assume il 
to be fluency ; for the scale for marking reading in 
his Bareme ^Instruction is based upon the frequency 
of such pauses as are not necessary to elucidate the 
meaning of the passage read. The examinees an 
classified according as they pause after the letters, 
the syllables, the words or the phrases. More 
recent investigators, discriminating between the 
silent reading we do for our own use and pleasure 
and the oral reading we do for the benefit of others, 
claim the former to be the more important, anc 
select the comprehension of the material read as 
the first essential, and speed of reading as the second. 
Compared with these, intonation, expression and 
pauses are regarded as unimportant. For this 
point of view there is much to be said. It is signifi- 
cant of that happy change which is taking place 
in our schools — the change from reading as an 
elocutionary display (a very indifferent one at best) 
to reading as a pleasurable pursuit. But compre- 
hension is a difficult thing to measure ; and it pre- 
supposes a more rudimentary ability which is quite 
easy to measure — the ability to translate certain 

134 



READING 135 



visual symbols into sounds, whether those sounds 
are actually produced or are merely imagined. This 
is the basal ability — the sine qua non of reading — ■ 
the step which no amount of intelligence would 
enable the learner to dispense with. His intelligence 
will, of course, eke it out ; it will enable him to 
anticipate coming words, to respond to slighter 
cues ; but ultimately his power to read is rooted 
in his ability to translate symbols into sounds, and 
this fundamental ability is what I here set out to 
measure. It is not the whole of reading ; but it 
is the basal and indispensable part, and it is the part 
which best lends itself to exact measurement. 

The test I adopted after some preliminary experi- 
ments is given on the following page : — 

The pupil was given a paper on which the test 
was printed as shown, and was asked to read as fast 
and as carefully as he could until he was told to 
stop. The number of words correctly read in a 
minute — that is, the total number read minus the 
number misread — gave the score. If the examinee 
hesitated for more than five seconds over a word 
and did not seem to be on the point of saying it, he 
was prompted and told to pass on, that particular 
word counting as an error. He was thus prevented 
from being too heavily penalised by his inability 
to recognise one or two particular words. 

It is quite clear that the test does not take intelli- 
gence into account ; it is designed to measure the 
bare mechanical art of reading — the degree of 
facility with which a pupil can translate the symbols 
of the simplest and commonest words of the mother 
tongue into the words themselves. Sense material 
was discarded as tending to confuse the issue. If 



136 MENTAL TESTS 

One Minute Reading Test 

is me on at by so us an it or be 
to as he of in go up am if no we 
my ox do the and for but him 
are can she dog let you not was 
out try see mix cat now boy saw 
bit met top run man pet lot get 
did van bad red cup bee lit pin 
had ran pen nut big old yet rob 
gun leg fun lip new fog has sit 
sly wig mud box ink sat end cut 
pay fed who six lad wet dry cow 
his peg tin say eat any far set bud 
kid pup fox ask egg cab ill use jam 
all pit got sad tea sky one yes fur 
act toe her our ten arm rock gone feel 
that rich till long flat this part foot 
made upon came mile back sand time 
said then wall into were done walk 
much loss seem went with come 



READING 137 



an intelligent lad, for instance, starts reading a 
fairy tale which begins " Once upon a time," the 
recognition of the first word brings inference into 
play, and the rest of the phrase is largely a matter 
of memory. But no such intelligent anticipation 
is possible in the test used ; each word, standing 
isolated in meaning, has to be read without any help 
from the context. It has to be read, not inferred. 

Much scorn has been levelled at this type of 
reading. It has even been denied that it is reading 
at all, and has been contemptuously called " barking 
at print." But my investigation tends to show that 
this mechanical response to the seen word, this bark- 
ing at print — call it what you will — is not only the 
basis of all reading, good as well as bad, but is also 
a trustworthy criterion of the interest with which 
reading is followed as a pursuit. 

As a test common to children of different schools 
and different ages, it possesses many points of 
advantage. Familiarity with subject-matter, which 
must always be a variable and disturbing factor 
where sense material is used, does not enter into 
the question ; there is no subject-matter. A 
peculiar knowledge of uncommon words avails 
nothing : there are no uncommon words. How- 
ever young a child may be, however rudimentary 
his knowledge, if he can read at all, he can read some 
of the words in the first three lines ; for all the 
common two-letter words in the language are to 
be found there. And however proficient a child 
may be he will find the task of reading the whole 
of the 158 words in one minute quite as much as he 
can accomplish. 

But these a 'priori reasons in favour of the test 



138 MENTAL TESTS 

do not dispense with the necessity of testing the 
test — of comparing, for instance, the results obtained 
by using this test with those obtained by using sense 
material, such as an " unseen " passage in the ordinary 
school reader. Such a comparison I carefully made 
with ten boys of about eight years of age. The 
mode of scoring was in each case the same — the 
number of words correctly read in one minute. 
The first point to be noted is that although 32 per 
cent, more words were read per minute in the con- 
tinuous prose than in my test, the order of merit 
was, with one trifling exception, the same in both 
cases. To test one kind of reading is virtually to 
test the other. The second point to be noted is 
that the discrete material gives a higher degree of 
reliability or steadiness ; for when the children were 
put to read the same passages again after five minutes 
interval, they improved but 7 per cent, with the 
discrete words as compared with an improvement 
of 22 per cent, with the continuous prose. The 
7 per cent, improvement was perhaps entirely due 
to a loss of nervousness ; but most of the improve- 
ment in the other case was doubtless due to the 
acquired familiarity with the meaning. As a test, 
therefore, the discrete words are better suited for 
repeated use. 

In estimating the speed of reading, it is well to 
be clear what precisely we are measuring. For 
there are four possibilities. We may measure the 
normal or the maximal speed of either oral or silent 
reading. The speed measured in this test is the 
maximal for oral reading. 

The question may be raised : how far is the 
recorded speed a real index of the speed of reading 



READING 139 



as distinct from speed of articulation ? There 
is little doubt that adults can read silently very 
much faster than they can read aloud — very much 
faster than they can articulate the words. But 
this is not true of a young child. I found by testing 
a number of children of 7 years of age that they 
could speak or recite at the rate of 170 words per 
minute while they read the test words at the rate 
of 40 per minute. Again, girls of 9I years old who 
read 80 words per minute were able to recite 220 
words per minute. 

The following norms were obtained by applying 
the test to the children of 49 schools : — 

Age. 6 yrs. 7 yrs. 8 yrs. 9 yrs. 10 yrs. 14 yrs. 

Boy's Score. 13 33 53 72 85 115 
Girl's Score. 15 38 58 j6 88 122 

The original experiment stopped at 10 years 
of age ; for I did not regard the test as suitable 
for older children, with whom the mastery of the 
mechanical factor may as a rule be taken for granted ; 
but as an afterthought I extended it so as to include 
children of 14. The results show a considerable 
flattening of the curve after 10. 

Among the 49 schools I included 10 which were 
reputed to be attended by the poorest children 
in London, and 9 situated in good residential 
areas. The results show that both boys and girls 
in good neighbourhoods are about 6 months (10 
marks) in advance of the average ; and in poor neigh- 
bourhoods the boys are 3 months behind, and the 
girls 6 months. Thus for the extreme types of 
home we find a difference of 9 months for boys 



140 MENTAL TESTS 

and 12 months for girls. A girl of 8 in Dulwich 
can read as well as a girl of 9 in Bermondsey. 

Through the courtesy of a friend, I was enabled 
to secure results from 6 elementary schools in Lan- 
cashire. In general tendency they tallied with the 
London results ; but the Lancashire boys were 3 
months ahead of London boys, and the girls 4 months 
ahead. The 6 schools, however, included no poor 
schools, and there is reason to believe that the social 
conditions were above the average. 

There is nothing to indicate whether the superi- 
ority of the children from good homes is due to 
heredity or environment — to higher native ability 
or to better opportunities. Both probably con- 
tribute. 

The statistics obtained lend support to the popular 
belief that girls read better than boys. Generally 
speaking, they are 5 marks or 3 months ahead. But 
it is a curious fact that this difference does not 
obtain in slum neighbourhoods. There the boys 
read quite as well as the girls. This is not merely 
true of the ten schools taken in a lump ; but, with 
one exception, of each of the 10 schools individually. 
Whatever the reason may be, whether it is due to 
the girls being more fully employed minding the 
baby — there generally is a baby — or doing domestic 
work, or whether this intrinsic sex difference does 
not hold good generally, the fact itself seems to 
admit of little doubt. 

Occasionally a reader rushed through the test 
with little regard to accuracy, and thus made a 
fairly high score in spite of many blunders ; whilst 
another reader would proceed more cautiously 
and secure a lower score although he made no 



READING 141 



blunders at all. The majority, however, maintained 
a steady level of cautiousness ; and on an average 
about three mistakes were made by children of all 
ages. This means that accuracy improved with 
age, and was roughly proportional to speed ; for 
to get three mistakes out of 88 words read (see score 
for girls of 10) was nearly six times as creditable as 
to get three mistakes out of 15 words read (score 
for girls of 6). 

The method of teaching reading in all the schools 
tested was some form of the phonic. The alpha- 
betical method pure and simple may be said to be 
obsolete in London, although the children are 
generally taught the conventional names of the letters 
either at the same time as their phonic values or 
after the art of reading has been at least partly 
acquired. The look-and-say mode of reading into 
which all other forms ultimately merge, is to a 
greater or lesser degree incorporated in the other 
systems. In fact, the system in vogue is mixed, 
with the phonic element predominating. There 
are, however, various forms of the phonic method 
current, some simple and some complex. Perhaps 
the most systematic and complex of all is the Dale 
method ; and in 19 out of the 49 schools this method 
is followed. Do the scores at these 19 schools afford 
evidence of the superiority of this system ? How 
do they compare with the scores at the 30 non- 
Dale schools ? Taken as a whole the Dale boys 
are 1 month behind when they are under 7 years 
of age, and 2 months in advance after 7 ; while 
the girls are 2 months behind when under 7, and 
2 months ahead after 7. But 5 of the 19 Dale 
schools are included in the 9 schools above referred 



142 



MENTAL TESTS 



to as situated in the wealthier neighbourhoods. 
And if the influence of home and district be elimin- 
ated it is doubtful whether the Dale results are as 
good as the non-Dale. It is certain that they are 
no better. Here is a system of high repute, regarded 
indeed by some as the mark of up-to-dateness in 
infant teaching — a system requiring special training 
on the part of the teacher, and involving the use 
of special apparatus and special books ; but judging 
from the results achieved, it is no better as a means 
of teaching reading than the ordinary phonic system 
in common use. It is true that it has other merits. 
It includes other things besides reading proper, 
such as printing, drawing, and phonetic analysis — 
things in themselves valuable ; but taken purely 
from the reading point of view, it fails to substantiate 
the high claim generally made on its behalf. 

What then is the salient characteristic of method 
in the schools where the test shows reading to be 
exceptionally good ? It is this. In the good schools 
reading is encouraged as a pursuit, and not merely 
taught in a series of lessons. The children read 
for the sake of the story, not for the sake of reading. 
It is a pleasurable occupation, and not a tiresome 
phonetic drill, nor yet an elocutionary display. 
Phonetic drill and elocution have their place in 
school routine, but the root of proficient reading 
grows in other soil. In the school where the reading 
is best of all, even children of six read small fairy 
tale books for pleasure. 

There is one arresting exception to the above 
generalisation. In a certain infants' school where 
no private reading takes place, but a large amount 
of word-building is taken on the blackboard, the 



READING 143 



result reaches high-water mark ; but in the senior 
school the curve sinks to the normal : the proficiency 
is not maintained. It will thus be seen that the 
same apparent results may be obtained in the earlier 
period by opposed methods ; but while the momen- 
tum is kept up by the one method, it is lost by the 
other. As ever, it is a question of interest. 

It should be clearly understood that this test, 
consisting as it does of words of no connected mean- 
ing, is intended to be used as a test only, and never 
as material for practice, nor even as suggesting 
the type of material for practice ; for I strongly 
hold the view that in selecting reading-books for 
children, subject matter is a consideration of supreme 
importance. If the subject is of no interest to 
the child, if it would not grip his attention when read 
to him instead of by him, then we must regard it to 
be of the wrong sort ; unless, indeed, we reject the 
view that the main aim and purpose of the teacher 
of reading should be to hasten the coming of the 
time when the child will spontaneously take up 
a book and read it for the sake of what it has to 
tell him. 

Although the test is oral, it must not be inferred 
that practice should be entirely oral, or indeed 
mainly oral. For the out-of-school reading, for 
which the school reading is a preparation and a 
training, is almost entirely silent : it is reading as a 
device for getting ideas. And the training of any 
specific activity should always, as far as possible, 
take the form of that activity. It is not always 
possible. At the earliest stage of reading, for instance, 
much drudgery in associating symbols with sounds 
is necessary before the process is sufficiently mechan- 



144 MENTAL TESTS 

ised for the sense of what is read to stand out clearly 
and predominantly in the mind. Indeed, for some 
time, the child, unless he reads aloud — unless there 
is somebody for whom he feels he is doing something 
— will not read at all. But the sooner this stage 
is passed the better. 

Again, fluent reading, regarded merely from the 
mechanical point of view, is mainly a matter of 
practice, and the amount of practice given in school, 
especially where individual class reading — reading 
in turns — is adopted, is so small that many years 
pass before a fair degree of fluency is attained. 

The reasons are now clear why I regard this test 
as useful for the early stages of reading only. As 
the child grows older the aspect of reading which 
becomes increasingly important is the extent to 
which it can be employed as a thought-getting 
device — the accuracy and rapidity with which the 
child absorbs the meaning of what he reads privately. 

It has often been pointed out that to read 
mechanically is one thing ; to understand what is 
read, another. And although it will be granted 
that a child may do the former without the latter, 
it is equally certain that he can never do the latter 
without the former. Until, indeed, a child can 
read about loo of the test words per minute, the 
mechanical art of reading cannot be said to have 
been completely mastered ; and the utilisation 
of the test is profitable as a means of measuring 
his fluency ; which is roughly a measure of the 
practice he has had ; which, again, is roughly a 
measure of the interest he takes in reading. Beyond 
that stage other tests overshadow the mechanical 
one. Reading, indeed, cannot in any sense be 



READING 145 



regarded as a simple process, nor can the same means 
be adopted for measuring proficiency in the earlier 
and later stages of acquiring the art. 

B. — As a Means of Acquiring Ideas 

At the age of nine most children have acquired 
a fair degree of facility in the mechanical art of 
reading. Henceforth reading is to them either 
an elocutionary exercise (reading aloud), or a means 
of getting ideas (silent reading). And of these 
two the more important is the latter. It is no 
exaggeration to say that in adult life ninety-nine 
out of every hundred books are read silently. The 
essential aim, therefore, in the teaching of reading, 
should be to give the pupil the power to absorb 
meaning from the printed page. If he is to gain 
either pleasure or profit he must understand what 
he reads. And the measure of his progress in under- 
standing is virtually the measure of his progress 
in reading. But how are we to measure understand- 
ing ? It is clear that the time-element cannot be 
ignored. What we have to determine is the rate 
at which the pupil can master the meaning of a given 
piece of prose or poetry. 

There are in use, in the United States, at least 
eight different types of silent reading tests. They 
generally consist in allowing the pupil a fixed time 
to read a given passage, and then ascertaining how 
much of the meaning can be reproduced. But 
here we encounter the difficulty that makes com- 
position so hard to assess. How can we weigh 
ideas ? How can we measure meaning ? Daniel 
Starch, in his silent reading tests, tries to get over 

L 



146 MENTAL TESTS 

the difficulty by getting the pupil to write out 
what he remembers of the passage read, and by 
counting the number of words written which cor- 
rectly express the thought. This is equivalent 
to marking a piece of composition by its length. 
Some of the other systems require a complicated 
key by which the reproductions may be scored. 
The scheme, however, which seems to be most 
widely used in America, is the Kansas Silent Reading 
Scale. It comprises a series of sixteen exercises 
which carry marks proportional to their difficulty. 
Exercise 6, for instance, which is valued at 2*3, 
runs as follows : " In going to school James has to 
pass John's house, but does not pass Frank's. If 
Harry goes to school with James, whose house 
will Harry pass, John's or Frank's ? . . . " The 
examinee has to fill in the blank at the end. This 
question is typical of the series — a series which 
admittedly tests reasoning : but does it test reading ? 
The pupil's mind is required not merely to follow 
the meaning of the sentence, but to go beyond it ; 
and it is quite conceivable that a child may be able 
to follow a plain narrative with ease and rapidity, 
and yet be very slow at dealing with puzzles of 
the Kansas kind. In any case the exercises differ 
in toto from the kind of matter people generally 
read. The last book one thinks of reading is a book 
of conundrums. 

Another peculiarity common to the American 
silent reading tests, is that more than one series 
is used. There is generally one for the lower grades, 
one for the middle grades, and one for the higher 
grades. And although the several series are supposed 
to be so adjusted in the matter of difficulty, that 



READING 14- 



the norms for the various school grades increase 
regularly, the adjustment is in point of fact never 
perfect. In the Kansas tests, for instance, the norms 
for Grade V and Grade VI are nearly the same. 

There is, further, the outstanding disadvantage 
to the Englishman, that the tests and results are 
arranged by grades and not by ages. The scale is 
never, except by precarious inference, an age scale. 

The test I have devised for my own use is as 
follows : — 

Silent Reading Test 
(3 Minutes) 

One fine morning in spring a robin flew down 
to the brink of a stream to quench his thirst. See- 
ing a trout in the water he began to talk to him. 
" I have often wondered," said he, " how you manage 
to keep alive. If I tried to stay under water like 
you I should be dead in a few minutes. And even 
supposing I could remain alive I should feel miserably 
cold in the chilly water without either fur or feathers. 
Please tell me why you are not drowned, and why 
you do not perish with cold." " You should never 
ask two questions at once," said the trout. " Quite 
right ! " croaked an old crow who had heard their 
conversation and had alighted on the bank beside 
the robin. He was very old and very wise and very 
inquisitive. Some thought that it was because he 
was inquisitive that he was so wise, others thought 
that his wisdom came from age and experience. 
Certain it was that he was regarded as the most 
learned of all the birds of his time, and that he 
used such long words that the little birds, beasts 
and fishes could rarely understand what he was 



148 MENTAL TESTS 

talking about. To return to the robin's questions, 
the trout replied : " Why don't I get drowned ? 
Why, one does not drown in the water : one drowns 
in the air." " Nonsense ! " said the robin. But the 
crow looked so severely at him that he trembled, 
and drooped his tail by way of apology. " As for 
feeling cold," continued the trout, " I don't know 
what you mean." The robin was about to say 
" Liar ! " when he caught the crow's eye and 
restrained himself. Then the crow, having held up 
his right foot to enjoin silence and attention, delivered 
himself thus : " It was held by Aristotle, and his 
opinion is confirmed by modern scientific theory, 
that there is no living creature that can exist in 
any and every environment : each requires sur- 
roundings suitable to its bodily structure and its 
bodily functions. To secure a supply of oxygen, 
which is necessary to maintain the purity and tem- 
perature of the blood, each animal is provided with 
organs which are adapted for extracting this element 
from the atmosphere, where it is present in great 
abundance. In land animals lungs serve that 
purpose ; in fishes, gills. Gills are so constructed 
that they can only take up the oxygen that is dis- 
solved in water. In the air the gills adhere together 
and the poor fish dies of asphyxiation. Our friend 
the trout was therefore quite justified in asserting 
that the atmosphere drowns fishes. As for his 
avowed ignorance of the distinction between heat 
and cold, we must not rashly accuse him of false- 
hood. It is a well-known psychological fact that 
sensitiveness to heat and cold is dependent on certain 
specialised nerve endings in the skin." He paused 
here to see the effect of his oration on his audience. 



READING 149 



While speaking he had been gradually closing his 
eyes in order to think better ; but at this point he 
opened them wide and found to his disgust that the 
trout had disappeared and that the robin was strug- 
gling with a big fat worm about twenty yards away. 

A double sheet, with the story printed inside, is 
distributed, and the children told that they will be 
given three minutes to read it, and that they will 
afterwards be tested to see how much they can 
remember. On the word of command the children 
must open the papers and read silently. At the 
end of three minutes the papers are collected and 
the following completion test given out to each 
child, with instructions to supply the missing words 
except those marked (x). 

Completion Test 
(Unlimited Time) 

One fine morning in (1) a (2) flew down to 
the brink of a ( 3 ) to quench his thirst. Seeing a 
( 4 ) in the water he began to talk to him. " I 
have often wondered," said he, " how you manage 
to (5) (6). If I tried to stay under water like 
you I should be dead in a few minutes. And even 
supposing I could remain ( x ) I should feel miserably 
( 7 ) in the ( x ) water without either ( 8 ) or ( 9 ). 
Please tell me why you are not ( 10 ), and why you 
do not perish with (x)." "You should never 
ask ( 11 ) questions at once," said the ( x ). " Quite 
right ! " (12) an old ( 13 ) who had heard their 
conversation and had alighted on the bank beside 
the ( x). He wg§ very ( 14) and very ( 15 ) and 



150 



MENTAL TESTS 



very ( 16.) Some thought that it was because he 
was ( x ) that he was so ( x ) ; others thought that 
his (17) came from (18) and (19). Certain 
it was that he was regarded as the most ( 20 ) of 
all the birds of his time, and that he used such ( 21 ) 
( 22 ) that the little birds, beasts and fishes could 
( 23 ) understand what he was talking about. To 
return to the ( x ) questions, the ( x ) replied : 
" Why don't I get drowned ? Why, one does not 
drown in the ( 24 ) : one drowns in the ( 25 )." 
"(26)" said the (x). But the (x) looked so 
( 27 ) at him that he ( 28 ), and drooped his tail by 
way of ( 29 ). " As for feeling ( x )," continued the 
( x ), "I don't know what you mean." The ( x ) 
was about to say " ( 30 )," when he caught the 
( x ) eye and ( 31 ) himself. Then the ( x ), having 
held up his right foot to enjoin ( 32 ) and ( 33 ), 
delivered himself thus : " It was held by ( 34 ), 
and his opinion is (35) by (36) scientific theory, 
that there is no living creature that can exist in 
any and every ( 37) : each requires (38) suitable 
to its bodily ( 39 ) and its bodily ( 40 ). To secure 
a supply of ( 41 ), which is necessary to maintain 
the ( 42 ) and ( 43 ) of the ( 44 ), each animal is 
provided with ( 45 ) which are adapted for extracting 
this ( 46 ) from the ( 47 ), where it is present in 
great ( 48 ). In land animals (49) serve that pur- 
pose ; in fishes, ( 50 ). ( x ) are so constructed 
that they can only take up the ( x) that is ( 51 ) in 
water. In the air the ( x) adhere together and the 
poor fish dies of ( 52 ). Our friend the trout was 
therefore quite ( 53 ) in asserting that the atmosphere 
(54) fishes. As for his avowed (55) of the dis- 
tinction between (56) and (57), we must not 



READING 151 



rashly accuse him of ( 58 ). It is a well-known ( 59 ) 
fact that ( 60 ) to ( x ) and ( x ) is dependent on 
certain ( 61 ) nerve endings in the skin." He paused 
here to see the ( 62 ) of his ( 63 ) on his ( 64 ). While 
speaking he had been gradually closing his eyes 
in order to think better ; but at this point he opened 
them wide and found to his ( 65 ) that the ( x ) had 
(66) and that the ( x ) was struggling with a big 
fat worm about (6j) yards away. 

The most convenient way to administer the com- 
pletion test, is to distribute strips of paper upon 
which the missing words are to be written. If the 
lines on the paper are numbered from 1 to 67 it will 
facilitate marking. One mark is awarded for each 
word correctly given. As it is a test of substance 
memory, and not rote memory, synonymous words 
are accepted. General terms, however, must not 
be regarded as substitutes for particular terms. 

The following synonyms and variations are per- 
missible : 3, brook, river ; 5, remain ; 5 and 6, 
exist; 8 and 9, in either order; 12, said; 14, 15 
and 16, in any order; 18 and 19 in either order; 
21, big; 23, hardly, scarcely; 25, atmosphere; 27, 
sharply, crossly; 31 checked, stopped; 35, upheld; 
38, conditions ; 39 and 40, in either order ; 42 
and 43, in either order ; 43, heat ; 46, oxygen ; 
47, air ; 48, quantities ; 52, asphyxia, suffocation ; 
53, right, correct ; 56 and 57, in either order ; 58, 
lying, untruth; 61, special, particular; 63, speech, 
words ; 64, listeners, hearers ; 66, gone, vanished. 
In every other case the exact word must be given. 

This test has the merit of being simple and work- 
able, of being applicable to all readers from the ages 
of nine to ninety, and of being objective in the 



152 



MENTAL TESTS 



sense that two independent examiners will, if they 
follow the instructions, inevitably give the same 
mark for the same achievement. The examiner may, 
if he wishes, examine himself. It will be seen that 
the narrative is easy to begin with, and gradually 
increases in difficulty, so that the dullest reader 
will be able to remember some, and the brightest 
fail to remember all. I have tried as far as possible 
to select, as missing words, those which indicate 
that the meaning of the text has been understood, 
and yet are not such as an intelligent pupil would 
infer from the context. The first blank, for instance, 
cannot be filled by reasoning, for there are many 
possibilities. The missing word may be " Summer," 
or " April," or any other season or month. And 
the second word may be any one of the numerous 
species of birds or insects. In fact, the missing 
words are not inevitable words : they really test 
whether the pupil has read the piece, has understood 
it, and has remembered it. 

To prevent the examinee from inferring the 
missing words at the beginning of the piece from 
what is said later on, I have omitted the words 
that afford a ground for retrospective inference 
and substituted ( x ). If, for instance, I had printed 
" trout " instead of ( x ) in the twelfth line, a shrewd 
lad would at once know that the fourth missing 
word was " trout." In order to ascertain experi- 
mentally, to what extent inference could supply 
the place of direct knowledge acquired from actually 
reading the piece, I submitted the second paper 
to a number of intelligent children who had not 
read the first. In no instance were more than three 
words guessed correctly. 



READING 153 



By applying the test to about 5000 children from 
nine to fifteen years of age, I arrived at the following 
norms : — 

Age. 9 yrs. 10 yrs. n yrs. 12 yrs. 13 yrs. 14 yrs. 

Score. 6 10 14 17 19 21 

Through the courtesy of Miss Lloyd Evans, the 
Principal of the Furzedown Training College, I 
was able to test the students in training. They 
made an average score of 41. 

The mean variations for the various ages from 
nine to fourteen were successively 3*5,' 5*3, 6"l, 
6, 6-i, 6-3. 

For the training college students it was 6. 

It has been urged in criticism of the test that it 
measures not understanding but memory. My 
reply is that it measures both ; and in measuring 
both it measures the actual intellectual gain got 
from the exercise. Indeed, the two factors are 
both inseparable and indispensable. If a reader 
forgets the meaning of the earlier sentences he cannot 
possibly grasp the meaning of the later sentences. 
Any word he reads may turn out to be key-word 
on which the significance of all that follows depends ; 
and if the key-word, or at least its meaning, be 
forgotten, his reading becomes vain. Sometimes 
the key-word comes late and modifies the sense 
of all that precedes it ; and if what precedes is 
forgotten, the point and significance of the whole 
piece is missed. Browning affords many instances 
of this kind. The key to " My Last Duchess," 
for example, is to be found a few lines from the 
end. The hint that the Duke contemplates a 
second marriage illumines all that he has previously 



154 MENTAL TESTS 

said, giving it point and purpose, and turning the 
poem into an intelligible whole. 

Again, if the reader will refer to my absurdity 
test on p. 38, he will see that the absurdities all 
occur in the latter half, and their detection depends 
on an exact remembrance of what is said in the first 
half. Not a single sentence is absurd in itself : 
it is only absurd when brought into relation with 
the rest ; and if the incompatibility is to be seen, 
the rest must be remembered. 

Admitting, however, that it is impossible to 
understand the piece without also to a large extent 
remembering it, is it not possible to remember it 
without understanding it ? It is possible, but so 
highly improbable that the possibility need not be 
seriously considered. It is only necessary to imagine 
a similar test given in Latin to an intelligent lad 
who knows no Latin, but can only read the words 
as though they were English, to see the futility of 
supposing a mere verbal memory to be of much 
service in a three minutes' test of this kind. For 
all practical purposes, if the subject understands 
the narrative, he will be able to supply the missing 
words ; and, conversely, if he remembers the missing 
words, it will be due to the fact that he has under- 
stood the narrative. 



CHAPTER IX 

SPELLING 

The usual mode of testing spelling in school is 
by means of an " unseen " piece of dictation. 
The main objection to this procedure is that the 
piece given is not standardised : its difficulty is 
unknown. And passages of prose vary so enor- 
mously in difficulty that to lay down any general 
rule regarding the number of mistakes per line 
that might reasonably be allowed at different ages 
is clearly impossible. 

Opinions differ respecting the range of words 
which a child should be expected to spell. Some 
think that he should never be required to spell 
words outside his own vocabulary, and that his 
written composition should be the only basis on 
which his ability to spell should be estimated. To 
this view it may be objected that a child's vocabu- 
lary is a growing thing, and it would be well to 
anticipate a little and to teach him to spell words 
which he will probably want to use in the near 
future. Moreover, it is sometimes necessary to 
write from dictation, or to record in notes the 
sayings of others ; and if the writer's own vocabulary 
is very limited, or restricted to certain favourite 
words (as in fact most people's vocabulary is), the 
range of his spelling vocabulary should be extended 

*53 



156 MENTAL TESTS 

so as to include the words that are in most common 
use. Thus we have two overlapping groups of 
words whose spelling should be known : first, those 
which constitute the pupil's speaking and writing 
vocabulary ; secondly, those most frequently used 
by the nation as a whole. But which are the words 
most frequently used ? And how many of them 
are we to include ? 

In America these questions have been answered 
by Dr. L. P. Ayres, who has compiled a list of the 
thousand commonest words in the English language, 
or rather the American variety of the English 
language. The method employed was to examine 
written material of various types, such as letters, 
newspapers, and children's compositions, and to 
make a list of the words used and the number of 
times each word occurred. Ayres combined the 
results of four such studies, which comprised 368,000 
words written by 2500 different persons. Some 
interesting facts emerged. It was found, for in- 
stance, that fifty of the words were used so fre- 
quently that they made up about half of the 
material examined. In order to secure a thousand 
words it was necessary to include words which only 
occurred once every 8000 words. 

By testing a large number of children with this 
list Ayres was able to divide the words into twenty- 
six groups, named after the letters of the alphabet. 
The words in each group (the groups vary con- 
siderably in size) are supposed to be of equal diffi- 
culty. The following list comprises the words in 
Group N. The percentages of these words that 
should, according to Ayres, be spelt correctly in 
the grades from III to VIII are 58, 79, 88, 94, 



SPELLING 157 



98 and 100 respectively. Translated into English 
terminology it means roughly that Standard II 
children should be able to spell 58 per cent, of the 
words, Standard III 79 per cent., and so forth. 

Ayres' Spelling Test 

Group N. — Except, aunt, capture, wrote, else, 
bridge, offer, suffer, built, centre, front, rule, carry, 
chain, death, learn, wonder, tire, pair, check, prove, 
heard, inspect, itself, always, something, write, 
expect, need, thus, woman, young, fair, dollar, 
evening, plan, broke, feel, sure, least, sorry, press, 
God, teacher, November, subject, April, history, 
cause, study, himself, matter, use, thought, person, 
nor, January, mean, vote, court, copy, act, been, 
yesterday, among, question, doctor, hear, size, 
December, dozen, there, tax, number, October, 
reason, fifth. 

The most useful list for English schools is Mr. 
Burt's, which I append — 

Burt's Graded Spelling Test 

Age. 

5.— a it cat to and the on up if box 
6. — run bad but will pin cap men got 

to-day this. 
7. — table even fill black only coming sorry 

done lesson smoke. 
8. — money sugar number bright ticket speak 

yellow doctor sometimes already. 
9.— rough raise scrape manner publish touch 

feel answer several towel. 



i 5 8 



MENTAL TESTS 



10. — surface pleasant saucer whistle razor 
vegetable improvement succeed begin- 
ning accident. 

ii. — decide business carriage rogue receive 
usually pigeon practical quantity 
knuckle. 

12. — distinguish experience disease sympathy 
illegal responsible agriculture intelligent 
artificial peculiar. 

13. — luxurious conceited leopard barbarian 
occasion disappoint necessary treacher- 
ous descendant precipice. 

14. — virtuous memoranda glazier circuit de- 
cision mosquito promiscuous assassinate 
embarrassing tyrannous. 

Note. — " The words assigned to any given age are 
those answered correctly by 40 to 60 per cent, of the 
age-group specified. Thus, approximately, 50 per 
cent, aged 10 last birthday can spell ' surface ' . . . 
' accident.' Therefore, to attain a mental age of 
ioi a child should spell fifty-five words, *". e. all to 
' vegetable ' inclusive (or the equivalent). 

" It is not necessary that all the children should 
be given all the words : twenty or thirty from the 
appropriate consecutive ages are usually sufficient. 
The mental ages assigned to the earlier words are 
somewhat arbitrary owing to wide differences in 
infants' schools." 

A protest should be made against the frequency 
with which unseen pieces of dictation are given in 
the higher standards of English elementary schools. 
Sometimes two lessons per week are devoted to it 
in the top class. The defence generally made is 



SPELLING 159 



that the children are backward in spelling ; to 
which it may be replied that dictation is primarily 
a test, a means of measurement, and not a means, 
except indirectly, of teaching spelling. At any rate 
it is not the most economical means. When a child 
suffers from malnutrition we do not try to fatten 
him by weighing him twice a week. 



CHAPTER X 

ARITHMETIC 

(a) The Fundamental Processes 

Several attempts have been made in America to 
standardise tests in Arithmetic. The most widely 
used, the Courtis Tests, share with all the rest the 
defect of insularity : they constitute a grade-scale 
and not an age-scale, and the monetary units are 
dollars and cents and not pounds, shillings and pence. 

Little has been done to establish norms suitable 
for England. In 191 3 and 1914 I carried out an 
extensive research into the ability of London children 
to perform the simple fundamental processes of 
adding, subtracting, multiplying and dividing. The 
results of this research were published in the 
Journal of Experimental Pedagogy for December 
1914 and March 1915. The tests were repeated 
and the standards broadly confirmed by Mr. P. L. 
Gray, H.M.I., in the schools of Leeds. The copy 
of the Journal (June 191 5) which contained Mr. 
Gray's account of his experiment also contained a 
criticism of my tests by the editor, Professor J. A. 
Green. At the meeting of the British Association 
at Newcastle in 191 6 the Report of the Committee 
on the Mental and Physical Factors involved in 
Education dealt with Norms in Mechanical Arith- 
metic and gave an account of investigations in 

160 



ARITHMETIC 161 



London and Sheffield on similar lines to my own. 
The tests used (they were devised by Mr. Cyril 
Burt) were better than mine. Mine suffered from 
the defect of being too brief. Five minutes were 
allowed for working twenty-four sums, and in nearly 
every school tested some of the older children finished 
the paper before the time was up. If the paper had 
been longer their score would have been higher. 

In the autumn of 191 9 I revised my original tests 
and administered them to a large number of London 
children. They differ in important respects from 
the 1914 tests. They are both simpler and more 
searching. The time allowed is three minutes 
instead of five, and none of the children tested were 
able to complete the papers within the time. A 
yearly age-scale is substituted for a half-yearly 
age-scale. Finally, the numbers have been so 
selected as to secure the greatest variety compatible 
with leaving all the sums of approximately equal 
difficulty. If a multiplication table be constructed 
up to 9 times 9, and a similar table for each of 
the other processes, every item in those tables will 
be found represented somewhere in the examples 
set ; generally twice, once in the first half and once 
in the second. 

Addition : Three Minutes 



64 


35 


82 


78 


46 


27 


3 


16 


29 


63 


92 


58 


56 


98 


31 


40 


9 


5o 


7i 


93 


5i 


98 


78 


H 


63 


42 


16 


43 


2 


5i 


23 


17 


39 


72 


19 


75 


47 


65 


89 


4 


80 


65 



M 



1 62 MENTAL TESTS 



70 


44 


86 


39 


81 


24 


16 


28 


8 


97 


85 


5o 


69 


92 


76 


57 


42 


16 


72 


92 


35 


52 


26 


5o 


46 


24 


5 


48 


13 


4 1 


13 


9 


68 


74 


70 


89 


93 


72 


53 


73 


38 


13 


29 


36 


7 


5i 


89 


40 


21 


81 


90 


24 


85 


73 


49 


5 


6 


54 


19 


24 


15 


58 


18 


47 


18 


57 


39 


24 


24 


58 


58 


63 


26 


66 


16 


79 


73 


72 


59 


38 


70 


3 


63 


64 


92 


16 


27 


34 


53 


69 


75 


15 


37 


3i 


16 


27 


92 


43 


70 


4 


96 


52 


69 


28 


82 


48 


48 


80 


79 


15 


15 


68 


29 


95 


58 


48 


34 


73 


7 


36 


24 


27 


8 


78 


40 


94 



Subtraction : Three Minutes 

69152 80031 68703 54218 
48729 63175 37956 49221 



17690 91435 62098 761 12 
7948 23256 34089 57346 





ARITHMETIC 


163 


85694 

2787 


60321 
H359 


70592 
26819 


80941 
53437 


78580 

29395 


6021 1 
437 l6 


81427 
42078 


93505 
16693 


74816 
53 6l 7 


92240 
59830 


80134 
46965 


75702 
28139 


78265 
2495 


70124 
65139 


80367 
20548 


94521 
16973 


35172 
19438 


59203 
47689 


69375 

7089 


49315 
19782 




Multiplication : 


Three Minutes 




273905 
4 


360197 

7 


59H7 2 
5 


465239 
6 


629175 
2 


196704 
9 


297836 
3 


519824 
8 


148637 
4 


254879 

7 


368051 

5 


780147 
6 



164 



MENTAL TESTS 



308465 328547 541783 736582 
2938 



612549 598162 561923 726493 
7465 



598263 
9 



793428 439716 



625097 
3 



180493 



641857 
5 



834729 
4 



582736 
7 



Division : Three Mitiutes 
4/26930 7/ 66 759 5/4 8l 75 6/44957 



2/365H 9/534 12 3/28103 8/58849 



4/5779 2 7/ r 3°26 5/82947 6/33802 



2/12978 9/16743 3/24861 8/85390 



7/59304 4/21 1 59 6/52298 5/63772 



ARITHMETIC 165 



9/24419 2/18758 8/39857 3/55378 



5/19238 7/ 8 9 2 9 2 9/34 26 3 4/7 82 95 



The examples were graphed or cyclostyled and 
distributed face downwards, one process at a time. 
Three minutes were allowed for working, and one 
mark allowed for each sum that was absolutely 
correct. 

The following norms were arrived at — 



L b 



Number of Sums right in Three Minutes 
Age. 9yrs. 10 yrs. nyrs. 12 yrs. 13 yrs. i4yrs. 

Addition ... 3 4 5 6 7 8 

Subtraction . . 2 3i 4i 5i 6J 7 

Multiplication 1^ 3 \\ 5I 6f 7I 

Division . . . 1 2f 4 5i 6J 7 

If we mark the papers in another way and 
instead of counting the number of sums right 
count the number of operations right, we shall get 
a more exact score, for examples partly correct 
would score marks. By operations I mean pro- 
cesses of the kind tested. For instance, in the first 
addition example there are ten addition operations, 
in the first subtraction example five subtraction 
operations. For multiplication and division the 
corresponding numbers are six and four. The 
advantage of giving the norms in operations per 
minute, as in the following table, is that in applying 
a rough test any examples may be set by the teacher, 
provided he makes a little allowance for the size of 



1 66 MENTAL TESTS 

the sums, and the time taken in writing the figures 
and in passing from one sum to another. 

Number oj Operations per Minute 

Age. 9yrs. ioyrs. nyrs. 12 yrs. I3yrs, i4yrs. 

Addition ... 12 16 20 24 27 30 

Subtraction .. 4 6 8 10 12 13 

Multiplication. . 4 7 10 12 14 16 

Division ... 2 4 6 8 9 10 

When reduced thus to operations per minute the 
results of my 191 9 investigation confirm the results 
I obtained in 191 4. 

Comments on the Addition Test. — The improve- 
ment with age is only partly due to a more facile 
application of the same method : it is mainly due 
to a change of method, to a gradual supersession of 
habits of a lower order by habits of a higher order. 
The lowest habit of all is that of adding by units ; 
the highest, that of adding en bloc. For example, 
in adding the series 8 + 5 + 9 + 2 + 7+1 the pupil 
working by the former method would start 8 + I + 
1 + 1 + 1 + I, etc., while the pupil working by the 
latter would say 8 + 5 =13 as a mere matter of rote 
memory. Between these two extremes there are 
various intermediary stages. Some, for instance, 
decompose the addends in order to form tens. 
Thus 8 + 5 = 8 + 2+3 = 10 + 3 = 13. Adding the 
next item, 13 + 9= 13 + 7 + 2 = 20 + 2 = 22, etc. 
Some other devices used to avoid counting by units 
are also based upon the decomposition of the 
addends into groups that can be added without 
further reduction. Then there is the method of 
arriving at the result by noting how far it falls 



ARITHMETIC 167 



short of a readily ascertained sum. For instance, 
13 + 9=13 + 10 — 1 ; and 8 + 7 = 8 + 8 — 1. Lastly, 
there is the method advocated in some schools of 
searching along the column for numbers which 
form tens. Thus in the series given above the 8 
and the 2 would be coupled, and also the 9 and the 
I. This is a useful device when the paired numbers 
come together ; but to link them when widely 
separated is to increase unnecessarily the mental 
strain, and to run the risk of omitting or duplicating 
some of the addends. 

There can be little doubt therefore that the 
most efficient method is that of adding the items 
seriatim and memoriter — as they come and by the 
addition table. Advantage should, of course, be 
taken of any obvious ten-group that would appear, 
but there should be no hunting for it. It has been 
maintained by some that to add 4 + 9 as 4+ 10— 1 
is more " intelligent " than to say straight off 
4 + 9 = 13. But why should it be so ? There is 
an assumption that 4 + 10 is known, while 4 + 9 is 
not. Logically the proposition 4 + 9 = 13 rests on 
the number system, 1, 2, 3, 4, etc., and counting by 
units is, in a sense, the one and only " intelligent " 
method — the one and only method that lays bare 
the ultimate ground of the proposition. But it is 
assumed that the rationale of adding is clearly 
understood by the pupils ; and the question under 
discussion is not the most explicitly logical but the 
most expeditious mode of adding. As a step 
towards memorising 4 + 9 = 13, the operation 
4 + 10 — I may be permitted ; but the process is 
not complete from the point of view of practical 
efficiency till it is short-circuited into 4 + 9 = 13. 



1 68 MENTAL TESTS 

The number of items to be thus memorised is not 
great. For if 4 + 9 = 13 be learnt, the sums of all 
such combinations as 14 and 9, 29 and 4, etc., are 
easily inferred therefrom. 

The time taken to work the addition paper gives 
a clue to the method used. I have applied the test 
to a few children without imposing a time limit. 
The children handed in their papers as soon as 
they were finished, and the time taken was recorded 
thereon. Later on each child was privately asked 
to work through one of the sums orally, in order 
that the method adopted might be ascertained. 
The results confirmed the view that both speed 
and accuracy depend upon the grade of habit upon 
which the process of adding is based. 

The danger of forming bad habits of computation 
is far greater in addition than in multiplication. 
In working the latter there is little temptation to 
count. The veriest tyro cannot fail to perceive 
the enormous labour-saving advantage of remem- 
bering that 6 X 8 = 48 over the counting of six 
eights ; but the advantage of memorising 6 + 8 = 14 
is not so obvious when the result can readily be 
arrived at by a mechanical drumming with the 
fingers. It is indeed a notorious fact that a certain 
percentage of educated adults count on the fingers 
■ — when nobody is watching them. 

Comments on the Subtraction Test. — The most 
salient feature of the subtraction results is the 
evidence afforded of the superiority from a prac- 
tical point of view of the method of equal addition 
over the method of decomposition. In my account 
of the 1 91 4 investigation I gave abundant evidence 
to this effect, evidence which is further strengthened 



ARITHMETIC 169 

by 1117 recent investigation. When the subtraction 
score was in any school markedly below the scores 
for the other three processes 1 guessed that the 
method of decomposition was taught at that school ; 
and my guess was always right. Let me take as an 
example one of the best schools tested. Situated 
in a very good residential district, it is attended 
by children of exceptional advantages. The girls' 
school is noted for the general thoroughness of the 
work. Now observe the difference in the results 
obtained in the two departments both at the lowest 
age and the highest age tested. 

+ - x -=- 

9 ^ rs -\Girls 7-3 3-8 & 3 47 

i4.vni B °y s 6 " 8 7 * 6 7 " 8 7 ' 2 

* 7 '\Girls io - 2 87 li"4 io - 3 

An examination of these figures will show that 
the girls' school, where the method of decomposi- 
tion is adopted, is, in spite of the excellent teaching 
labouring under a heavy disadvantage as compared 
with the boys' school, where the method of equal 
additions is taught. The figures also illustrate the 
fact that although the advantage of one system 
over the other tends to diminish with the age of 
the children, the advantage is never lost — not at 
any rate during the elementary school period. 

But the disparity in the practical efficacy of the 
two methods is really greater than would appear 
from the above account ; for the examples set having 
few or no noughts in the minuends failed to bring 
out the more glaring disadvantages of the decom- 
position method. When, however, such an example 



i jo MENTAL TESTS 

as 40,000 — 197 is set, the ineptitude of the method 
is more strikingly revealed. Even in the highest 
classes of the decomposition schools the time taken 
to work such an example is excessive, and the degree 
of accuracy abnormally low. And yet it is examples 
of this type (where the minuend is a round number) 
that are of most frequent occurrence in everyday 
life. This is obviously so in the case of money. 
We want change from a five-pound note, a sovereign, 
a half-sovereign, or a shilling, and not from such a 
collection of coins as is represented in ^4 13J. J%d. 
The reason for the inferiority of the decomposi- 
tion method is not far to seek. In the equal 
addition method the compensation is made — 
accounts are squared — at the very first number 
dealt with after the minuend has been disturbed. 
In subtracting 37 from 85, after taking 7 from 15 
the disturbed relationship of difference between 
minuend and subtrahend is immediately restored 
by increasing the 3 tens to 4 tens. In the method 
of decomposition, however, it is the 8, the second 
figure dealt with, that has to be changed to restore 
the balance. If the minuend figure is zero the 
balancing of accounts is still longer deferred. In a 
phrase, the main secret of the difference lies in the 
dispatch with which accounts are settled. One is 
" cash payment," the other " credit." And the 
postponement of the compensating act increases the 
chances of its fulfilment being forgotten. But this 
is not the only point of difference between the two 
methods, for there is a further disparity in the area 
of disturbance. When the figure in the minuend 
represents a smaller number than the corresponding 
figure in the subtrahend it is necessary to disturb 



ARITHMETIC 171 



the minuend (method of decomposition) or both 
minuend and subtrahend (method of equal addition). 
In the latter case it is never necessary to disturb 
more than two figures ; in the former it is always 
necessary to disturb two, and sometimes many more ; 
and for a young child to bear the many changes in 
mind is no easy task. 

The disadvantage of the decomposition method is 
not of course limited to pure subtraction sums : it 
vitiates all exercises into which subtraction enters. 
Long division, for instance, is, as I have abundantly 
tested, performed in decomposition schools with 
difficulty and with dubious accuracy. 

And yet the decomposition method is apparently 
taught in about two-thirds of the London schools. 
What is the reason for its popularity ? It is not 
the method we learnt in our youth ; it does not 
seem to be the method adopted by the adult, even 
when he has learnt that method at school. The 
reason is to be found in its greater intelligibility. 
It is easier for a child to understand the decom- 
position of numbers than to grasp and apply the 
principle that the difference between two numbers 
remains unchanged if the same number be added 
to both. It is therefore the favourite method in 
the infant school, and the senior school follows the 
lead. But granted its greater intelligibility, its 
practical efficiency is not encouraging. The younger 
the child the more is he shackled by the inferior 
method. Unless, indeed, we assume that some of 
the older children in the decomposition schools 
discover in some indirect way the equal addition 
method and use it in preference. It is not often 
that one finds a class of older children all of whom 



172 MENTAL TESTS 

practise the decomposition method. Do we not 
in any case pay too great a price for a doubtful 
boon ? If at first the child sees the rationale of 
the process of decomposing the minuend, he soon 
gets to perform it automatically. The " intelli- 
gence " supposed to be concerned is a temporary 
illumination only. Indeed for pure practical effi- 
cacy it is better that the rationale should not, at 
the actual time of working, be thought of at all. 
The pupil should confine his efforts to a rigid 
application of the rule. I have frequently observed 
that when teachers in training are asked to work a 
subtraction sum and explain the steps, they fre- 
quently give the right reason but the wrong answer. 
It may be pointed out that an intelligent appli- 
cation of an arithmetic rule does not necessarily 
mean a scientific knowledge of the underlying prin- 
ciples. A child may learn to walk and to put the 
power to intelligent uses without knowing anything 
about the mechanism by which walking is achieved. 
So may he learn to work subtraction by rule of 
thumb, and be able to apply it quite intelligently 
to the practical purposes of life. He may later on 
study the physiology of walking, or the logical basis 
of the rule ; but there is no more reason to think 
that he will compute better in the latter case than 
there is for thinking that he will walk better in the 
former. This is not a plea for the mechanical 
teaching of subtraction ; but it is a plea for regarding 
subtraction as primarily an instrument to be placed 
in the hands of the young pupil for the purpose of 
solving certain problems of actual life. If he can 
understand, the reasons for the steps taken, well and 
good. If not, he should for the present use it 



ARITHMETIC 173 



without understanding it. Indeed I have long 
contended that during the last year or so of an 
elementary pupil's schooling he should be taught 
the underlying principles of all the rules he has 
learnt. Attempts should, of course, be made to 
render the rules intelligible at the time of learning ; 
but the teacher should be in the main content if 
the pupil can use these rules in concrete cases. A 
critical examination of " long division," for instance, 
is a valuable exercise for a lad of 13 — far more 
valuable than the senseless manipulation of symbols 
which often passes for algebra. The mathematics 
for the last year of the school life of an elementary 
pupil should include the assimilation of all the 
undigested material in the whole arithmetic course, 
if that course is, as it should be, regarded as a 
systematic study of the principles of numbers. 

It has frequently been asserted that there is a 
third method of teaching subtraction — the method 
of complementary addition. But this is not, like 
the two methods just dealt with, a device for 
meeting the difficulty of " borrowing " : it is an 
alternative way of looking at the process of sub- 
traction itself. 16—7 may mean either : (a) what 
is left when 7 is taken away from 16? or (b) what 
must be added to 7 to make 16 ? If the latter view 
be adopted then subtraction is regarded as com- 
plementary addition — as a solution of the equation 
a -+- x — b. 

It may be remarked about this form of subtrac- 
tion that it is not taught as a general process in any 
of our schools, at least not to my knowledge. It 
is true that complementary addition sometimes 
appears in a hybrid form. Thus 43 — 26 is some- 



i 7 4 MENTAL TESTS 

times worked in this way : 6 from 10 leaves 4, 
4 and 3 are 7, etc. But such roundabout methods, 
in which two steps are taken where only one is 
necessary, are not to be commended. 

Complementary addition pure and simple, com- 
bined with equal addition as a " borrowing " device, 
is advocated at some of the Universities, especially 
where much work in logarithms has to be done. 
Instances are known where greater speed and 
accuracy have resulted from a change from the 
subtractive to the additive attitude. 

The additive view is strongly urged by the few 
head teachers who have tried it. They think that 
the subtraction method should be discovered by 
the child : the steps being indicated by the following 
examples — 

Step I. 4x1 Step II. xx\ Step III. 

xc^Vadd. 4 7/ add. r 43 

86 J 4 7] add. 

H3 \ 

159 xx] 



The " carrying " or compensating step is naturally 
adopted, with no need for more explanation than 
the " carrying " in simple addition. 

It is not for me to judge this method on a priori 
grounds, but its advantages are sufficiently obvious 
for us to declare a true bill in its favour and give it 
at least an experimental chance. 

On the Importance of Tables. — It has already been 
shown that the facility in working addition and 
subtraction mainly depends upon a ready knowledge 
of the addition table. 



ARITHMETIC 175 



The complete table may be written in this form — 

1+1= 2 

2+1= 3 2+2= 4. 

3 + 1= 4 3 + 2= 5 3+3= 6 

4 + 1= 5 4+2= 6 4+3= 7 4+4= 8 

5 + 1= 6 5+2= 7 5+3= 8 5+4= 9 5+5=io 

6+1= 7 6 + 2= 8 6+4= 9 6+4=10 6 + 5=11 6+6=12 

7+1= 8 7+2= 9 7+3 = 1° 7+4=ii 7+5 = 12 7+6=13 7+7=14 

8+1= 9 8-t 2=10 8+3 = 11 8+4=12 8+5=13 8+6=14 8 + 7=15 8+8=16 

9 + 1 = 10 9+2=11 9 + 3=12 9+4=13 9+5=14 9+6=15 9 + 7=i6 9+8 = 17 9+9 = 18 

It will thus be seen that there are 45 results to be 
memorised — 45 habits to be fixed — it being under- 
stood that each of the above items represents four 
processes. Thus 8 + 4=12 should also be memor- 
ised as 4+8=12, 12 — 8 = 4 and 12 — 4=8; 
not of course as independent processes, but as 
necessarily implied in the one formula 8 + 4= 12. 

The same remarks apply to the multiplication table, 
except that there are only 36 items to be learnt. 

There are some educationists who contend that 
the tables should not be memorised. In so saying 
they do not mean that they should not ultimately 
be memorised ; but rather that no conscious effort 
should be made to memorise them. The results 
should be arrived at either — 

(a) By building them up afresh each time, or 

(b) By referring to a table book. 

If they are continually being built up afresh, any 
intellectual value such a process may originally 
possess soon disappears. It sinks to the level of 
the merest mechanical work. And if this method 
is to be applied to the multiplication table, logic- 
ally it should be applied to the addition table as 
well, and counting by units should always be 
encouraged. 

If, on the other hand, it is merelv meant that the 



176 MENTAL TESTS 

results should be calculated ab initio each time until 
they are fixed in the memory, experience shows that 
the mere habit of doing so tends to form a stronger 
tendency to start the process than to recall the 
result. Older children, for instance, who count on 
their fingers delay indefinitely the counting by 
groups. No effort is made to memorise the results, 
and in consequence they elude the memory. Indeed 
a far shorter way of reaching the goal is afforded 
by the second alternative, that of using a table- 
book — assuming, of course, that the construction 
of the tables is understood. Whenever, for in- 
stance, the product of 7 and 8 is needed the table 
is looked at. Here the mind attends exclusively to 
the result, 56, and is not absorbed in attending to 
the process. Mr. Winch has experimental evidence 
to show that if a large number of examples involving 
the use of a specific table are worked rapidly by the 
pupils who have this table in front of them, it is 
actually memorised better than if a conscious effort 
is made to memorise it without working examples. 1 

It seems clear that progress in mathematics is 
made possible by assuming the results of previous 
processes and using these results as stepping-stones 
to still higher results. 

On the Best Method of Memorising the Tables. — 
The addition table has generally been left to look 
after itself, but the multiplication table has always 
received a certain amount of attention. In bygone 
days it was systematically memorised by frequent 
simultaneous repetition ; and even at present the 
chanting of the tables, although less widely adopted, 

1 See also Kirkpatrick : " Memorising versus Incidental Learn- 
ing," J. of E due. Psychol, v. 7, 405-412. 



ARITHMETIC 177 



is almost the only means that is employed. But 
this chanting of the tables is open to several 
objections. 

Memorising of all kinds depends upon the fixation 
of a habit-series ; and the limits of the series should 
be clearly defined. Each formula, such as 4 x 7 = 
28, constitutes a self-contained system, and it 
should be so memorised as to be completely usable 
without reference to preceding formulae. In other 
words no unnecessary associations should be set up. 
To associate by rote memory 4x5 with 4x6, and 
4x6 with 4 x 7, etc., is a superfluous, if not an 
injurious, bit of mental mechanisation. Chanting 
tends to establish these useless associations. 

Another objection is that the speed of this simul- 
taneous repetition is far too slow for the economic 
fixation of habit. The effect of speed upon 
mechanisation, although not generally recognised, 
is considerable. If, for instance, a passage of 
poetry has to be memorised so as to render its 
repetition automatic, the repetition of the lines at 
maximum speed has been found, in my own case 
at least, to diminish the number of repetitions 
necessary. It has probably something to do with 
the span of attention. 

A third objection to the simultaneous chanting of 
tables is based upon the liability of the attention to 
wander during the repetition. Attentive repetition 
is far more efficacious than the inattentive kind. 

Finally, there is the objection that may be urged 
against all kinds of simultaneous class work ; that is, 
that it makes no allowance for individual differences 
in the mode and rate of learning. 

There are experimental grounds for believing 

N 



178 MENTAL TESTS 

that the method of individual muttering — a method 
which unfortunately seems to " get on the nerves " 
of some teachers — is considerably more efficacious 
than the method of concerted repetition. 

There are two methods of memorising the tables 
which I have reason to think would prove effective 
— methods which are not exclusive but supple- 
mentary. Both might be tried. 

(1) Take, say, two items per diem in the addition 
table, such as 7 + 8 = 15 and 4 + 6 = 10 ; and two 
per diem in the multiplication table, such as 
7x8=56 and 4x6= 24. If this be systematic- 
ally done, and past work frequently revised, the 
whole will be learnt in less than five weeks. If 
only one of each be taken per day the whole can 
be mastered in less than three months. 

(2) Learn by applying. Put, for example, the 
7 times table before the boys and let them work 
very rapidly a large number of sums involving 
multiplication by 7. Of the two methods this is 
probably the better. 

On the Importance of Practice, and the Claim of 
the Individual. — That the principles of number 
should be intelligently taught ; that they should be 
recognised by the pupil as rooted in the experiences 
of everyday life ; that they should be learnt and 
applied with understanding ; that they should fre- 
quently be presented in novel combinations — these 
are matters upon which there is now no divergence 
of opinion. But when we ask the questions : 
Should every exercise be given in concrete form ? 
Should the problem dominate the arithmetic 
lesson ? we get a variety of answers. 

There are many who believe — there are more 



ARITHMETIC 179 



who wish, to believe — that sufficient practice in the 
mechanism of computation is gained by working 
problems and problems only. But whatever opinion 
one may have held ten years ago on this matter, if 
one has followed the recent development of mathe- 
matics in the elementary schools one cannot help 
being forced to the conclusion that such practice is 
insufficient. Ciphering, in its rudimentary forms, 
is so useful an art that proficiency therein is justly 
regarded as one of the essential aims of an ele- 
mentary school, and to discover the most economical 
means of achieving that aim, without doing violence 
to the pupils' instincts and interests, will ever be 
one of the central and vital problems of teaching. 

It is not fair to argue that since the excessive and 
exclusive grind at mechanical arithmetic which 
characterised the period of payment by results was 
distasteful to the pupils, mechanical arithmetic is 
in itself distasteful. Indeed, many children share 
the opinion of the little girl of my acquaintance 
who says that she likes sums but does not like 
sums about John. 

A noticeable feature of the present arithmetic 
course is the absence — or at least the infrequence — ■ 
of the pure practice or drill lesson. From having 
all the lessons practice lessons we have come down 
to none. The custom of wrapping up numbers in 
abundant verbiage has become so inveterate that 
the mere sight of a naked number gives some of us 
a sort of shock. Some time ago I was reproached 
by a teacher for asking a little girl in an infant 
school to add 2 and 3. All departure from the 
concrete has come to be regarded as wicked. We 
have in consequence an ounce of arithmetic to a 



180 MENTAL TESTS 

pound of padding. I have seen a teacher spend 
ten minutes over this little question in mental 
arithmetic : " If 80 birds sat on a tree, and 30 
of them flew away, how many would be left sitting 
on the tree ? " Laboriously she wrote it on the 
board, and persistently she checked all attempts at 
answering until she had explained the situation to 
the point of boredom. 

Another factor unfavourable to progress is the 
non-recognition of the essential heterogeneity of 
any collection of children, however carefully chosen. 
Any seeming homogeneity in a class is both super- 
ficial and temporary. However much the units 
may resemble one another in their present attain- 
ments they will differ enormously in their capacity 
for work, and consequently in their rate of improve- 
ment. If they appear like one another to-day, they 
will appear unlike one another to-morrow. Al- 
though this fact has been clearly demonstrated by 
others, 1 I have taken steps to verify it for myself. 
Three classes in a girls' school were allowed to work 
through the exercises in their arithmetic text-books 
at their own pace for half-an-hour per day. The 
results were as follows — 



Number in Class ..... 
Approximate age of Children 
Number of half-hour Lessons 
Average total number of sums worked 
correctly ..... 

Highest Score ..... 
Lowest Score ..... 
Mean Variation ..... 

1 See, for instance, Search's Ideal School, pp. 29 and 33. 





-Class , 


A 


B C 


5° 


46 42 


10 


12 13 


27 


26 23 


206 


145 181 


39° 


250 514 


95 


70 24 


57 


34 87 



ARITHMETIC 181 



It would be difficult to find a school more care- 
fully organised — a school where the children in a 
class were nearer the same level — and yet the varia- 
bility in their rates of working is seen to be enormous. 
In the highest class the best girl was able to work 
more than 21 times as fast as the worst ; and although 
this amount of disparity is exceptional, rarely will 
it be found that the fastest in the class does not 
work at least three times as rapidly as the slowest. 

It will be seen that, taking the three classes to- 
gether, on an average 7 sums per child were worked 
correctly in half-an-hour. Five girls in the top 
class were able to do more than double this average. 
It must not be thought that the exercises worked 
were of an easy type, or were of a merely mechanical 
nature ; they were continuous examples from 
McDougall's Suggestive Arithmetics ; and these 
books are above, rather than below, the average 
in difficulty. 

A careful investigation of the methods of teaching 
arithmetic at present in vogue in elementary schools 
has convinced me that the most serious and preva- 
lent defect is the excessive use of the blackboard, 
both for setting exercises to be worked by the class, 
and for exposition — for explaining, and exempli- 
fying, and correcting. 

When we consider that it is rare for a class working 
from examples written on a blackboard to get 
through more than four sums during a lesson of 
forty-five minutes (that is, half as long again as the 
lessons referred to above) it becomes obvious that 
the individual scholar is not working at anything 
like his normal pace. I do not go so far as to urge 
that a child should always work at the highest 



1 82 MENTAL TESTS 

pressure, but I do submit that he should sometimes 
do so. 

It is often the practice of the teacher to write 
an example on the board, and set the whole class 
to work it on paper. After all have finished (note 
the waste of time on the part of the brighter chil- 
dren) the sum is marked. If about one-third of 
the class gets it wrong, the teacher, as a rule, works 
it himself on the blackboard, or gets the class to 
work (or to seem to work) it with him. This is idle 
time for two-thirds of the class ; and it is not the 
best method of correction for the other third. 
More often than not the mistakes are due to care- 
lessness on the part of the pupil, or to an imperfect 
knowledge of the tables ; and effective correction 
depends on individual effort rather than on black- 
board explanation. 

An arithmetic lesson is occasionally taken up by 
the teacher working one or two examples on the 
blackboard with the class, the children afterwards 
copying them out in their exercise books. The 
concerted appearance of this work is illusory. The 
work is really done by the teacher and a few of the 
more alert pupils. The copying out is of little 
value except as a relaxation from the boredom of 
watching other people work. 

These practices are by no means universal, nor 
do they imply that the instruction is mechanical 
and perfunctory. In making the criticisms it is but 
fair to record my conviction that earnest efforts are 
almost universally being made to vivify the instruc- 
tion and to bring it into line with modern educa- 
tional ideals, and that whatever faults exist are due 
not to lowness of aim, but rgther to a misconception 



ARITHMETIC 183 



of how a high ideal may best be approached. The 
spirit of the Suggestions to Teachers and of the 
Report of the L.C.C. Conference on Arithmetic has 
permeated the majority of schools, and is doing 
incalculable good ; but at the same time many 
sound practices of the past have sometimes been 
forgotten, and the new conditions that are develop- 
ing with the gradually diminishing class and the 
more rapid movement of pupils have not been met 
by a corresponding change of method. That 
change may briefly be described as a progress from 
class teaching to sectional teaching, and from 
sectional teaching to individual teaching — in fact 
from larger to smaller units. The ideal teaching is, 
of course, individual teaching, and Rousseau, in his 
Emile, assumes as a principle : one teacher, one pupil. 
It will be seen that " blackboarditis " (if I may 
be permitted to call it so) arises from too ardent 
and sanguine a desire to preserve the unity of the 
class — from the belief that the individuals forming 
this unity should work at the same rate, and progress 
at the same rate. One teacher with whom this 
matter was discussed not only held this doctrine, 
but strictly maintained that the pace should be 
that of the slowest pupil. This indeed seems to 
be the only logical form of the doctrine. It is 
clear that the average pupil (if there be such) 
cannot set the pace, as that would leave about half 
the class in the lurch. In actual practice a small 
number is recognised as forming no real part of the 
body of the class, and is labelled the " tail end." 
The " tail end " is left out of account, and the 
pace is virtually fixed by the slowest pupil among 
the remainder. 



1 84 MENTAL TESTS 

But it is clear from what has already been said 
that the doctrine of the homogeneous class ought 
to be abandoned, and the teachers should devise 
means of securing the maximum of healthy effect 
from each individual child. 

That it is necessary to devise such means is obvious 
when we consider the size of the class and the limited 
time and energy at the disposal of the teacher. He 
cannot possibly devote the necessary amount of 
personal attention to each child. The solution of 
the difficulty lies in the delegation of his powers, 
and in fostering in his pupils a sense of responsi- 
bility. We have not yet discovered the extent to 
which we can trust the pupils. By adopting a 
general policy of mistrust, by never allowing a child 
to mark his own, or even another child's, exercises, 
by making no child responsible for anybody's 
conduct or progress but his own, by retaining all 
corrective and coercive powers in the teacher's 
hands, we gain certain advantages : we simplify 
matters, we minimise the likelihood of abuse of 
authority, and we cultivate in the pupils the virtue 
of obedience. But we lose much more than we 
gain. We fail to secure normal and healthy 
progress, we fail to foster respect for an internal 
as distinct from an external authority, we fail to 
cultivate the power to rule wisely as a balance to 
the correlative virtue of obeying wisely, and we 
sacrifice the brilliant and the stupid to the mediocre. 
The surprise with which we view the success of the 
prefect system among elementary school children 
is itself a mark of our traditional mistrust. The 
possibilities of self-government and self-culture 
among school children will, I believe, when fully 



ARITHMETIC 185 



realised, provide the key to the solution of a large 
number of the difficulties which press upon the 
teacher at the present time, and which seem to 
put an abnormal strain upon his nervous system. 
I am not here concerned with showing how precisely 
this delegation of work and responsibility may be 
effected in the arithmetic lesson (each teacher can 
best discover this for himself), but with suggesting 
the direction in which the ideal of individual 
development probably lies. 

Recommendations. — In view of the facts and 
arguments set forth above, I venture to make the 
following definite recommendations — 

(1) That the tables, both addition and multi- 
plication, be by some means or other fixed in the 
memory early in the arithmetic course. 

(2) That the simultaneous repetition of the 
tables be superseded by individual learning, or 
better still, by their application to examples to be 
worked rapidly. 

(3) That seriatim repetition be discarded after 
the structure of the tables is understood. 

(4) That adding by tables be the final objective 
in practising addition, and that adding by units, 
or by partial groups, or through any roundabout 
device, be regarded as a habit of a lower order, to 
be abandoned as soon as habits of a higher order 
can be engendered. 

(5) That speed of adding be insisted on as a 
means of pressing forward towards the higher 
habits. 

(6) That the method of equal addition be uni- 
versally taught as the practical method of working 
subtraction, 



1 86 MENTAL TESTS 

(7) That the method of decomposition be re- 
garded, if taught at all, as a means of showing the 
correctness of the result arrived at by the usual 
method. 

(8) That at least one pure practice lesson be 
given per week. 

(9) That speed as well as accuracy be aimed at 
in the practice lesson. 

(10) That the terminal examination in arithmetic 
contain at least one straightforward abstract sum. 

(11) That each class be frequently practised in 
the work of all the lower classes. 

(12) That means be adopted to secure the progress 
of each pupil at his own natural rate. 

(13) That the blackboard be not used for setting 
out examples when text-books are available for 
that purpose ; nor for working sums which could 
easily be worked by the majority of the class ; nor 
for correcting errors due to mere carelessness. 
(The blackboard has, of course, its legitimate use 
for class and sectional teaching ; it is only when it 
becomes a means of preventing individual effort 
that its use is open to objection.) 

(14) That the practice of copying in the exercise 
books examples worked out on the board be 
discarded. 

(15) That much of the responsibility of marking 
exercises be, with due reservations and precautions, 
delegated to the pupils. 

(b) Simple Oral Arithmetic 

Many a teacher has felt the need of some simple 
means of estimating, with a reasonable degree of 



ARITHMETIC 



187 



precision, the arithmetical attainments of young 
children. The tests that have hitherto been 
published are intended for older children, for 
children who are able to work sums on paper. 
They cannot measure the beginnings, and are 
consequently of no use in dealing with children in 
infant schools. 

To meet this need I have used the following tests 
in addition and subtraction — 



One Minute Oral Addition Test 



(1) I + 2 


(11) 4 + 4 


(21) 7 + 5 


(2) 4 + 1 


(12) 5 + 2 


(22) 8 + 3 


(3) 2 + 2 


(13) 6 + 4 


(23) 4 + 9 


(4) 2 + 4 


(14) 1 + 8 


(24) 6 + 8 


(5) 3 + 2 


(i5) 3 + 7 


(25) 7 + 6 


(6) 4 + 3 


(16) 6 + 3 


(26) 9 + 8 


(7) 2 + 5 


(17) 2 + 6 


(27) 9 + 6 


(8) 5 + 4 


(18) 5 + 5 


(28) 8 + 7 


(9) 3 + 5 


(19) 7+2 


(29) 5 + 9 


(10) 8 + 2 


(20) 4+6 


(30) 7 + 9 


One Minute Oral Subtrt 


iction Test 


(i) 2- I 


(11) 8 — 2 


(21) 11 — 2 


(2) 3 - 2 


(12) 7-5 


(22) 10 — 6 


(3) 5 - 1 


(13) 8-3 


(23) 12 — 3 


(4) 6 - 2 


(H) 7-4 


(24) 1 1 — 6 


(5) 5 - 3 


(15) 9-3 


(25) 12 - s 


(6) 2-2 


(16) 8-5 


(26) 13—4 


(7) 7-2 


(17) 10-4 


(27) i5-9 


(8) 6 - 4 


(18) 9-5 


(28) 14 — 6 


(9) 7 - 3 


(19) 10 - 3 


(29) 17 - 8 


(10) 6 - 3 


(20) 9-4 


(30) 16-7 



MENTAL TESTS 



Each child is tested individually and in isolation. 
He is asked the question, " One and two ? " and as 
soon as he answers it he is asked the next, " Four 
and one ? " and so on. He is not allowed to proceed 
until he has given the right answer. The number 
of questions correctly answered in one minute 
gives the score. 

The same method is adopted for administering 
the subtraction test. 

A little preliminary questioning is desirable to 
put a child at his ease, and to see that he knows 
exactly what is required of him. 

The following norms are based on the results 
obtained by myself and others in the application 
of the tests to about ten thousand boys and girls 
within the last six years. 



Age. 


6 yrs. 


7 yrs. 


8 yrs. 


9 yrs. 


ioyrs 


Addition Score 


6 


10 


H 


18 


22 


Subtraction Score 


4 


7* 


II 


Hi 


18 



The mean variation seems to be nearly the same 
for each age group and for each process, and amounts 
to between three and four. 

The girls are able to add a trifle better than the 
boys, but in subtraction there is no appreciable 
difference between them. 

With the very youngest children the score is low, 
not merely because they are slow in computing, 
but because their knowledge is limited to the first 
few numbers in the scale. They cannot answer 
the whole of the questions even if they are given 
unlimited time. When, however, older children 
score few marks it is because they add by units. 
This points to the expediency of memorising the 



ARITHMETIC 189 



addition table early. The answering in a few 
schools, however, convince me that there is a danger 
of premature memorising. 2 + 5 = 10, for instance, 
is a type of answer by no means infrequent. This 
confusion between the addition and the multipli- 
cation tables is scarcely possible if the child is 
familiar with the make-up of the first ten natural 
numbers. 

In subtraction the question that seems to present 
the greatest difficulty is the sixth (2 — 2). 

As the oral examination of a large number of 
pupils took a considerable time it was hoped that 
a saving might be effected by setting the same test 
in written form. It was found however on actual 
trial that even with the older children the written 
test was a less delicate measure of arithmetical 
ability. The questions were typed and set to a 
number of children between nine and ten years 
of age, in the form given above with a blank space 
for the answer. The children between nine and a 
half and ten did 20 per cent, worse than at the oral 
examination, and the children between nine and 
nine and a half did 30 per cent, worse. The differ- 
ence would, it is reasonable to assume, be increasingly 
great as we went down the scale of age. It was 
therefore considered wiser, in dealing with such 
rudimentary work, to adhere to the oral form 
throughout. 

I have endeavoured to find the difference between 
the achievements in good and poor schools, the 
terms good and poor being used in a social sense 
only. Instead of comparing two schools, the best and 
the worst — a plan accompanied by obvious risk — a 
group of very good schools was compared with a 



190 MENTAL TESTS 

group of very poor schools. The difference proved 
to be greater than I had anticipated. In both 
addition and subtraction the good schools were at 
least one year in advance of the age-norms, and the 
poor schools at least one year behind. There was, 
in fact, a difference of more than two years between 
the achievements of the two social classes. 

I also found distinct evidence in support of what 
seems to be a general rule : the higher the social 
status the more favourably do the girls compare 
with the boys. In good neighbourhoods the girls 
compute a little better than the boys, in poor 
neighbourhoods a little worse. 

(c) Arithmetical Devices 

This test aims at discovering how many of the 
" rules " commonly taught in the elementary 
schools have been mastered. If the pupil shows 
that he knows the rule and has merely made a slip 
in computation the sum is counted right. Each 
correct sum scores one mark. 

Arithmetical Devices {unlimited time). 

(i) 658 x 204. 

(2) 95567 ^ 53. 

(3) & 14J. 5J x 26. 

(4) £ 2 3 "*■ 9\ d -+ I 7- 

(5) Calculate the cost of 15 tons 3 cwt. 2 qrs. at 

f\ $s. 6d. per ton. 

(6) i + f . 

(7) *» - f • 

(8) !xi 

(9) * ■*■ I- 



ARITHMETIC 191 



(10) -i x *i. 

(n) -6-^ -003. 

(12) 5 : 12 : : 9 : x. 

(13) Find the average of 5, 11, 7, 2, o, 19. 

(14) What is the value of £0-168 ? 

(15) Find the simple interest on £650 f° r 2 years 

It will be observed that where a simple example 
will suffice to indicate whether the pupil knows the 
rule the simple example is adopted. No. 5 and No. 
12 proved the most difficult ; due no doubt to the 
fact that within recent years " practice " has fallen 
into discredit, and proportion has given place to 
the method of unity. 

■Ai e - 9Y rs - 10 yrs. 11 yrs. 12 yrs. 13 yrs. 14 yrs. 

Score . . . \ 3 5 61 8 9J 

(d) Applied Arithmetic (Problems) 

To develop the capacity to apply the principles 
of numbers is after all the final aim of the teaching 
of arithmetic ; and the extent to which the pupil 
can bring his knowledge to bear upon the common 
affairs of life is the real measure of his understanding. 
Hence the importance which we now-a-days attach, 
and rightly attach, to " problems." It is regarded 
as questionable wisdom to reduce all problems to 
types and to teach them under the old system of 
rule and example. The root objection to this 
plan is that the pupil, recognising a particular 
problem (often by illegitimate signs) as belonging 
to a certain group, is liable to work it by rule of 
thumb rather than the direct application of basal 



192 MENTAL TESTS 

principles. It prevents him, in fact, from reasoning 
the thing out. If, however, pupils are to be trained 
at all in the solution of problems, it is necessary 
to call their attention to the underlying principles ; 
directly or indirectly they must be taught to recog- 
nise a certain sameness in the examples, and to 
do this is to systematise and classify. Take for 
example the 19th problem in the test given below. 
This is the same as asking : " What are the two 
numbers whose sum is 5 and whose difference is 
2 ? " Or again, " A bottle and a cork cost z\& ; 
the bottle cost 2d. more than the cork ; what did 
the cork cost ? " This, too, is cousin german to 
No. 10. The real danger lies not in the recognition 
of the type, but in working successively so many 
examples of the same type that the work becomes 
mechanical — a danger not difficult to avoid. 

At any rate, whatever objections there may be 
to the teacher's classifying problems for his pupils, 
there is a distinct advantage in his classifying them 
for himself. He should be familiar with the common 
applications of arithmetic, and should be careful 
both in teaching and testing to vary his types. 
He can never perhaps exhaust the types ; but he 
can readily make a catalogue of the commonest 
of them. The test below is, in fact, just such 
catalogue. It comprises twenty fundamental types 
of problems reduced to their simplest forms. It 
will be observed that the actual calculations are 
extremely easy ; for it is not computation that is 
being tested, but merely the capacity to applj 
principles. Hence a slip in counting is overlooked 
when the papers are marked, and every problem 
solved by the right method is allowed to score one. 



ARITHMETIC 193 



The problems are arranged in order of increasing 
difficulty — an order which differs from my precon- 
ceived notion of their difficulty, and which was 
discovered by actually applying them to a large 
number of children. 

Applied Arithmetic Test (unlimited time) 

1. If there are 100 apples on a tree and the wind 
blows down 1 7, how many are left on the tree ? 

2. Two hundred oranges are put into 5 baskets so 
that each basket has the same number of oranges. 
How many are there in each basket ? 

3. If a man earns .£5 y. 6d. in a week, how much 
will he have earned at the end of a month ? 

4. I want to buy a book which costs js. 6d., 
but I have only is. S^d. in my pocket. How much 
more money do I need ? 

5. John pays 8s. \d. for 5 lbs. of butter. What 
would Henry have to pay for 7 lbs. of the same 
butter ? 

6. If eggs sell at 3 for 2d., what will 2 dozen cost ? 

7. One day two boys earn ten shillings between 
them by carrying trunks from an hotel to a railway 
station. One boy carries 5 trunks during the day 
and the other 7. How ought they to share the 
money ? 

8. What is the least number that must be added to 
1483 to make it exactly divisible by 16 ? 

9. After spending a third of my money I find I 
have 3 j - . \d. left. How much had I at first ? 

10. Two girls had tea at a tea-shop. The waitress 
charged for both on one bill, which came to is. 6d. 
One girl had a threepenny cake more than the other. 
How much of the half-crown ought each to pay ? 

o 



i 9 4 MENTAL TESTS 

ii. A certain man can dig a garden in 3 days, 
and his son can do it in 6 days. If they both work 
together how long will they take ? 

12. Nine soldiers eat their food in one hut and 
15 in another. Seven loaves of bread are allowed 
for each hut. If the 9 soldiers in the first hut eat 
their bread in 4 days, how long will it take the 15 
soldiers to eat theirs, assuming that all soldiers eat 
the same amount ? 

13. A bankrupt pays 5.5". in the £. What did he 
owe to a creditor to whom he pays £16 10s? 

14. After the population of a town has decreased 
by 10 per cent, the number of people left is 18,000. 
How many were there at first ? 

15. A shopkeeper wishes to sell a blend of tea at 
is. 3d. a pound by mixing tea at 2s. a pound with tea 
at 3-f. a pound. In what proportion should he mix 
them ? 

16. If I lose 5 per cent, by selling an article for 
£9 ioj., what should I lose or gain per cent, by selling 
it for .£10 5-f. ? 

17. A, B and C cycle continuously round a 
circular track. A takes 8 minutes to go round, 
B 9 minutes, and C 12 minutes. If they all start 
together, how long will it be before they are all 
together again at the starting-point ? 

18. P and Q are two towns 210 miles apart. A 
train which travels at the rate of 30 miles an hour 
starts at 9 a.m. to go from P to Q. At the same 
time a train which travels at 40 miles an hour starts 
going from Q to P. When will these trains meet ? 

19. A man rows at the rate of 5 miles an hour 
with the stream, and 2 miles an hour against the 
stream. What is the rate of the stream ? 



ARITHMETIC 195 



20. A cyclist who rides at the rate of 12 miles 
an hour chases a man who walks at the rate of 3 miles 
an hour and who has had 2 hours' start. How long 
will it take the cyclist to catch the walker ? 

The norms are as follows — 



Age. 


9 yrs. 


10 yrs. 


n yrs. 


12 yrs. 


13 yrs. 


14 yrs 


Score 


2 


3i 


5 


61 


8 


9* 



The lowness of the level of achievement will 
probably surprise those who have not had a wide 
experience in setting arithmetical problems to chil- 
dren. It is possible that the results I obtained were 
somewhat vitiated by war conditions, and that it is 
desirable to revise the norms later on when the 
schools have completely recovered. Indeed, it is 
always expedient to make a periodical revision of 
scholastic standards, for these standards are the 
resultant of native intelligence, courses of study, 
and efficiency of teaching ; and two at least of these 
factors vary with time. 

The boys do better than the girls in applied 
arithmetic, but the difference in these simple 
problems is too slight to justify separate norms for 
the two sexes. 



CHAPTER XI 

PRACTICAL ABILITY 

We cannot test the mind as a whole : we can only- 
test it piecemeal. And in testing it piecemeal, it is 
found that certain specific abilities manifest a sort 
of kinship. They not only seem on the surface to 
be kindred abilities, but when tested they give 
results which are highly correlated. They form a 
natural group, clearly separated from other natural 
groups. Of the three such groups which are most 
readily discernible, literary ability seems to be the 
factor common to one, mathematical ability to 
another, and motor ability to the third. It is 
this third factor, the factor that underlies success in 
clrawing, handwriting and handwork, that here 
demands our attention. 

It seems reasonable to assume that success in all 
sorts of manual work depends on the general efficiency 
of one's motor apparatus. A man's body is many 
things at once. To the food-faddist it is a digestive 
tube, to the bacteriologist it is a happy hunting- 
ground for bacilli, to the boxer a fighting machine, 
to the philosopher a thinking machine, and to the 
craftsman a wonderfully complex and delicate 
instrument for making things. And the important 
point of application of the instrument is the hand. 
The hand is in fact taken as representing the whole 

196 



PRACTICAL ABILITY 197 

neuro-muscular system. And if we test the dexterity 
of the hand we are supposed to test motor ability 
as a whole. We must distinguish, however, between 
innate ability and acquired ability ; for it is the 
former that mainly interests the psychologist. The 
primary and basal test of motor ability has for its 
aim the discovery, not of the amount of motor 
skill that has been acquired by practice, but of the 
amount of aptitude for acquiring skill. It is the 
potentiality we wish to measure, not the actuality ; 
the original capital, not the interest that has accumu- 
lated through careful investment. Just as the aim of 
Binet's tests is to measure that general intellectual 
ability which islndependent of schooling, so the aim 
of a motor test is to measure that general motor 
ability that is independent of training. And the only 
test of this kind that has crept into general use among 
psychologists is the tapping test. 

Essentially the test consists in discovering the 
number of taps the unpractised subject can make per 
second. A pencil and a piece of paper roughly serves 
this purpose. It has, however, two disadvantages : 
the marks made are difficult to count, and the subject 
cannot be allowed to tap more than once on the 
same spot. For careful work a piece of apparatus 
is necessary which records automatically the number 
of taps made, whether made with a stylus on a flat 
surface, or by merely pressing a small lever after 
the manner of the telegraph operator. The claim 
of tapping to be regarded as a test of general motor 
ability is considerably strengthened if the results 
resemble in a broad way the results of intelligence 
tests — if they show a gradual improvement with age, 
if the maximum is reached during adolescence, 



198 MENTAL TESTS 

and if the effect of special training is negligible. The 
first two conditions are satisfied in the outcome of 
a research conducted by Miss Bickersteth at Oxford, 
and recorded in Vol. IX of the British Journal of 
Psychology. She tested girls from five to fifteen 
years of age and found that as they got older they 
gradually improved, from 3 taps per second at 
five years of age, to 5 taps per second at fourteen. 
Here the maximum was reached : girls of fifteen 
did no better than girls of fourteen. The third 
condition, that the score should be unaffected by 
practice, is fairly well satisfied. Miss Bickersteth 
found that the improvement produced by practice 
was very slight. Unfortunately, however, there is a 
marked disparity among the results obtained by 
different investigators. This is largely due to the 
fact that they use different instruments. The 
instrument I have myself used gives a higher score 
than that used by Miss Bickersteth. My score at 
the first trial was 7*4 taps per second. With a 
pencil, however, on a piece of paper my rate is 5*4. 
Several adults whom I have tested with the lever 
instrument score about 6-5, and girls of fifteen give 
on an average the same score as adults. It is a 
curious fact that the few expert pianists whom I 
tested did not tap any faster than the average. 
Neither did expert typists. 

Let us now consider a different kind of motor 
test, which is carried out with a piece of apparatus 
invented by Mr. McDougall of Oxford. The 
apparatus consists of a heavy brass plate with 24 raised 
sockets 2 centimetres high arranged in a circle. The 
subject has to insert a small steel plunger with a 
wooden handle into each socket as fast as he can ; 



PRACTICAL ABILITY 199 

and the time taken to go completely round gives 
the score. As the plunger exactly fits the socket, 
the skill required is the same as that involved in 
putting a key into a lock. Miss Bickersteth, who 
has experimented with this instrument, found that 
children of five took on an average 28 seconds, 
and children of twelve took 20 seconds. Beyond 
that age there was no improvement. Here again 
we have results following the same laws as those 
obtained by tapping. 

When, however, we compare the tapping scores 
with the plunger scores, we come against the amazing 
fact that there is virtually no connection between the 
two series. What slight correlation there is gradually 
decreases with age. In other words, a child who 
does well at the tapping test is just as likely to do 
ill at the plunger test as to do well. So that if one 
of these tests is a test of motor ability, the other is 
not ; for they give contradictory results. Looking 
closely at the two tests, however, we see that the 
plunger test introduces a new element. Tapping 
measures speed of movement only : the plunger 
test measures precision as well. In tapping we may 
aim as carelessly as we like, but with the plunger 
we must aim precisely. Moreover, tapping can be 
done blindfold, but the plunger test needs the co- 
ordination and co-operation of eye and hand. 
Motor ability, in fact, in any profitable sense of the 
term, is not a simple thing : it comprises at least 
three elements — strength, speed and precision. Any- 
body who goes to a fair can roughly test his strength 
at a machine and his accuracy of aim at a shooting 
booth ; but if he wants it done scientifically he 
must go to a psychological laboratory. There he 



zoo MENTAL TESTS 

will find a dynamometer and an ergogograph for 
testing his strength, and a dotting machine for testing 
his precision. 

Another simple motor test similar to the tapping 
test consists in the dealing of cards. The score is 
given by the number of cards dealt in a fixed time. 
Mr. Burt has used this test extensively, and has shown 
that it is positively correlated with other motor 
tests. It is found, too, as any one who has watched 
an old whist player dealing cards will readily believe, 
that practice affects the rapidity with winch it is 
done. 

There is one important point upon which all 
those who have carefully investigated these simple 
motor processes are agreed ; and that is that the 
connection between the simpler forms of motor 
ability and intelligence is much smaller than that 
shown by more complex motor processes. It is 
true that certain American investigators have 
arrived at different conclusions — have found a 
marked direct correspondence between mental and 
motor efficiency. But then they obtained their 
data from non-experimental sources. The only 
American who has investigated this matter by rigor- 
ous experiment is Bagley, and he found an inverse 
correspondence. The most careful researches of 
all have been made in England by Mr. Burt, Mr. 
Moore, Dr. Carey and Miss Bickersteth, and they 
all found a comparatively small amount of positive 
correlation between the two types of ability — an 
amount which got smaller and smaller as the subjects 
grew older, and more intelligent. With the older 
defective children the correlation is still high. 
This is not very surprising when we discover that 



PRACTICAL ABILITY 201 

the kind of ability revealed by these instruments — 
the tapping apparatus in particular — has apparently 
little connection even with skill in craftsmanship. 
From the few experiments that I have made (they 
are far too few to be conclusive) the children who 
are regarded as " clever with their fingers " cannot 
as a rule tap more rapidly than those whose " fingers 
are all thumbs." The only inference we can 
legitimately draw from these facts is that the simple 
motor tests I have described measure some specific 
ability which is not an index either of fine powers of 
craftsmanship or of high intellectuality. We cer- 
tainly have no right to infer that the ability in 
question is worthless. For the same line of reasoning 
would force us to admit that memory too was 
worthless. The correlation between rote memory 
and intelligence is not high : a fool sometimes has 
a good memory, and a genius a bad one. Yet we 
are bound to concede that the fool would have been 
a bigger fool if his memory had been worse, and the 
genius would have been a greater genius if his memory 
had been better. So with natural motor capacity, 
in however narrow a field it may work. There may 
be other things that are more serviceable even for 
technical skill ; but in itself it is good : it is better 
to have it than not to have it. 

The only use of tapping that cannot be impugned 
is as a means of determining whether a pupil is 
congenitally right-handed or left-handed. I myself 
am an inveterate dextral : I tap 7*4 to the second 
with the right hand, and 5*5 with the left. 

In experimenting with this instrument one cannot 
fail to be struck by the evenness of the scores. I 
dealt with five adults in succession who made 



202 MENTAL TESTS 



precisely the same score — 200 in half a minute. In 
Miss Bickersteth's experiments the mean variation 
for both the tapping and the plunger scores was 
surprisingly low as compared with the variation in 
the other abilities tested. In fact, we here seem to 
be testing a gift which among civilised races nature 
has distributed with rare impartiality. People 
differ very little in their basal motor endowment : 
it is in the use to which they put this endowment 
in the interests of the higher intellectual powers 
that wide differences appear. 

We cannot help feeling that we have not yet 
reached the root of the matter — that we have failed 
to put our finger on the essential thing in the making 
of a craftsman. And if native hand-skill is not the 
essential thing, what is the essential thing ? Let 
us examine a few significant instances. Vierge, a 
celebrated black-and-white artist, had the misfortune 
to lose the use of his right arm. In a short time he 
was producing drawings indistinguishable in execu- 
tive skill from those which he had formerly produced 
with his right. Mr. H. Weaver Hawkins, a young 
student at the Camberwell School of Arts and Crafts, 
was severely wounded during the war by shrapnel 
passing through his right arm-pit and penetrating 
his shoulder-blade. Pyaemia set in and attacked 
both shoulder-blades and both elbows. Surgical 
operations became necessary : the two elbow-joints 
were removed and artificial ones put in their place. 
The result was that when he got up from his bed of 
sickness he found his arm movements woefully 
restricted. He had little power in his shoulders, 
little control over his elbows, not much more over 
his wrists and fingers. He seemed like a man with 



PRACTICAL ABILITY 203 

two paralysed arms. But he soon found that he 
could move his left hand in one series of directions, 
and his right hand in another series of directions. 
So when he returned to school eighteen months 
ago, and took up his art studies again under Mr. 
Walter Bayes, he held his pencil in his less crippled 
hand — his left — and by eking out its movements with 
his right was able to make a start in re-learning the 
art of drawing. Now he can draw as well as he 
ever could. Indeed, his work, recently exhibited 
at the Goupil Gallery, was highly praised by critics 
who knew nothing of his infirmity. Requiring two 
hands to do imperfectly the work of one, and drawing 
as it were with his whole body, he manifests a strength 
and precision to be found only in the accomplished 
artist. Here we have a notable instance of the 
triumph of mind over matter. To thwart the 
creative impulse in such a man is impossible — unless 
you kill him. If his hands are gone, he will draw 
with his feet ; if his feet, too, are gone, he will draw 
with his elbow, his chin, his teeth — with any part 
of his person to which he can attach a pencil or a 
brush. If the essential spirit is within him it seems 
to create the machinery with which it works. In 
the long run it is brain that counts, not muscle. 
It is in the mind of man that artistry and craftsman- 
ship reside : they depend on a form of psychic or 
cerebral energy which flows out through the hand, 
the hand being the most permeable outlet ; but if 
this outlet is blocked the imprisoned energy will 
force open some other channel of escape. 

If, therefore, we try to gauge a person's capacity 
for making things by getting him to wag his finger, 
we must not be surprised to discover that we are 



204 MENTAL TESTS 

merely touching the fringe of a great matter. And 
whatever name we may give the primary essential 
we may be sure it is not a simple thing. For we 
shall find motor elements inextricably mixed up 
with intellectual elements of the highest order, and 
emotional elements of the subtlest form. To call 
the central aptitude constructive ability is certainly 
to connect it with one of the great instincts of 
humanity, but at the same time it masses under 
one name a number of distinct abilities which we 
have neither analysed nor measured ; and until we 
have measured them individually there is little 
hope of our being able to estimate them collectively, 
or, indeed, lay hold of that single factor (if there is 
such a factor) which may be supposed to be common 
to all these units. It has, however, been argued 
that as all construction in the handicrafts consists 
in adapting and arranging objects in space, a capacity 
to conceive and to picture those arrangements in 
the mind is at least part of the general constructive 
ability. One of Binet's intelligence tests for adults 
consists in folding a square of paper twice, cutting a 
triangular notch in one of the sides, and asking the 
subject to draw what it would look like if it were 
opened. 

A more complex construction test is that of the 
dissected cube. The subject is asked to imagine a 
painted cube of three-inch side cut into cubic 
inches, and is required to say how many of these 
little cubes are painted on three sides, how many 
on two, how many on one, and how many on none. 
Another way of administering the test is to present 
the twenty-seven small cubes all mixed up and ask the 
subject to put them together so as to form one large 



PRACTICAL ABILITY 205 

cube painted all over. A record is made of the plan 
adopted and the time taken. The subject who 
works in accordance with a premeditated plan is 
regarded as superior to the subject who works by trial 
and error. It is a difficult test, which can only be 
done with facility by what Terman calls " superior 
adults." 

The commonest type of construction test is the 
form board, of which there are many varieties. The 
essence of the problem is the same as that of the 
jig-saw puzzle : how to put things together to form 
a whole. The time taken gives the score. 

Mr. T. L. Kelly of Texas University has devised a 
construction ability test on the meccano principle. 
A quantity of material consisting of strips of wood of 
different shapes and sizes, and a variety of blocks 
and wheels, is placed before the pupil and he is 
asked to build the best thing he can out of them. 
Here initiative and inventiveness are brought into 
play. The test is reasonable enough and simple 
enough ; the difficulty lies in assessing the result — the 
same difficulty in fact that we have in working the 
models made in the handicraft centre. It is hard 
enough to mark them when all the things are the 
same : it is harder still when they are all different. 
In America they try to get over the difficulty by 
forming a standardised scale of specimens which 
have already been marked in accordance with the 
average judgment of a number of independent 
examiners. Any particular object to be marked 
has to be compared with the standard specimens 
until its equal is found. But it is not easy to find 
its equal. It is not easy to say whether an indiffer- 
ently made toy table is equal to. better than, or 



2o6 MENTAL TESTS 

worse than, a badly made parquetry mat. The 
specimen scale, in fact, does not do away with indi- 
vidual judgment, nor does it appreciably lessen the 
variability of marking. 

The test that seems to give the best evaluation of 
the factors which make up practical ability is the 
maze test. Mr. S. D. Porteus, the Director of 
Research at the Training School, Vineland, New 
Jersey, has invented a series of these tests, has stand- 
ardised them, and has compared the results with 
those obtained by using other types of tests. The 
correlation coefficients show that the Porteus tests, 
while yielding as a whole the same type of develop- 
mental curve as Binet's, differ widely from them in 
the estimates they afford of certain individuals who 
are mentally unstable and are temperamentally 
unfit to make their way in the world. Mr. Porteus, 
in fact, contends that the Binet tests are too ex- 
clusively intellectual, and that they generally fail 
to detect the children who have brains but no grit, 
who have linguistic ability but little common sense, 
who show a superficial brightness but have little 
capacity for forethought and planning. 

The accompanying diagram represents the Porteus 
test for children of 14 years and 6 months. It 
is one of the series of eleven standardised for the 
years from 3^ to 14^, no test being given for 13^. 
The problem is to trace with a pencil the most 
direct route of threading the maze by entering at 
S and getting out again by some other exit. The 
following are Mr. Porteus's instructions : " Show 
child starting-point at S, and tell him to find his way 
through the test form without going along any 
blocked path. As soon as a mistake is made, stop 



PRACTICAL ABILITY 



207 



the child and bring him back to the starting-point for 
his second trial. Never allow the child to retrace 
his course." Half-year credit is allowed if the test 
is passed on the second trial. If he passes on the first 




Porteus Test 



Year XIV 



trial his mental age is regarded as at least 14!, if 
on the second at least 14. 

A new line of investigation has recently been 
opened up in America, mainly by F. B., and 



208 MENTAL TESTS 

L. M. Gilbreth. It is technically termed " motion- 
study." Mr. Gilbreth made a systematic study of 
brick-laying, and found that a big reduction could 
be made in the number of separate movements 
involved. From eighteen they could be reduced to 
five ; with the result that 30 men could by the new 
method lay as many bricks as 1 00 men by the old 
method, and would be less fatigued at the end of 
the day. A brief account of this research will be 
found in Dr. Myers's Present-Day Applications 
of Psychology. This little book also describes the 
chronocyclegraph, an instrument for photographing 
a movement so that it can be examined in all its 
details, and the extent and speed of each part scien- 
tifically measured. By means of it an awkward 
action may be compared with a skilled action, so 
that the needless and harmful elements may be 
brought to light and eliminated. It bids fair to 
reveal to us in due time how we may learn to work 
efficiently and to play efficiently ; and perhaps 
allows us to indulge in the Utopian hope that the 
distinction between work and play may disappear 
altogether. With the drudgery part reduced and 
the creative part increased work will become the 
joy and delight we all feel it ought to be. 

The conclusion at which we arrive is that skill in 
carrying out any piece of practical work, needing as 
it does the thinking mind as well as the creating 
hand, involves a large number of special aptitudes 
and a large number of special habits ; and that mere 
motor ability, in the barest sense of that term, is only 
a part, and that not the most important part, of the 
whole process. Attempts to measure innate dex- 
terity have not so far proved of any help to the 



PRACTICAL ABILITY 209 

teacher ; nor have the methods of measuring the 
higher functions involved in constructive work 
developed sufficiently to give the young craftsman 
any guidance in pursuing his craft. We have not 
yet discovered a good indirect means of testing 
practical ability : we must test it directly. We must 
measure it as we have always measured it, by getting 
the pupil to do a piece of work and forming our 
estimate of it by standards which knowledge and 
experience have fixed in our minds. 



CHAPTER XII 

COMPOSITION 

There is no branch of study more important 
than English Composition, and there is none so 
hard to mark. So heavy, indeed, is the task, that 
teachers have been known to bargain with their 
chiefs about the minimum amount of marking to 
be done. In London Elementary Schools the mark- 
ing of one set of composition exercises per week is 
generally regarded as all that can be reasonably 
demanded of the class master. Some teachers do 
more, but this is looked upon as a work of superero- 
gation. Marking involves a twofold task — correct- 
ing the imperfections and appraising the result ; 
and of these, one seems endless and the other hope- 
less. And the corrections do not help us much in 
aiming at an estimate of the merit of the exercise. 
For to appraise a piece of writing by counting the 
blunders is itself a blunder. On this basis Shake- 
speare would fare badly, and Lamb would come 
off worse than if he had placed himself in the 
hands of the schoolmaster who wanted to teach 
him how to write essays. A pretentious piece of 
writing may have nothing in it — not even blunders ; 
and another piece may be full of good things, and 
at the same time full of faults. Not that faults 
do not matter, but that value is to be judged 

2IO 



COMPOSITION 211 

positively, not negatively — not by subtracting marks 
for each fault, but by adding marks for each 
merit. 

And the worst of the business is that the marker, 
after spending weary hours in toiling through a 
pile of papers, cannot rid himself of the suspicion 
that his labours are vain. He knows that the 
pupil, ignoring the emendations in red ink, will 
simply glance at the final mark and cast the paper 
aside. The corrections are made in the wrong 
place. The mistakes are removed from the paper, 
whereas they should be removed from the pupil's 
mind. The corrections are not made in the right 
place, because they are not made by the right 
person. For the right person is the pupil himself. 

How, then, can we make the task of correcting 
fall more upon the shoulders of the pupil who is 
benefited by it, and less upon the shoulders of the 
teacher who is bored by it ? To begin with, the 
pupil must have ideas. He should be put to write 
on those topics only which really occupy his mind. 
Every child thinks about something — constantly 
thinks about something — and that something, if 
it can be discovered, is the theme upon which he 
is best fitted to write. His ideas are best put 
when they come warm from his brain. Then 
only does writing become a means of self-expression. 
But since his ideas are often meagre and trivial, 
and the composition exercise is a means of en- 
larging both his circle of thought and his store of 
words, as well as of improving his control of what 
words he already has, he should constantly be 
encouraged to venture on new topics. And for 
this an opportunity for preparation is essential. 



212 MENTAL TESTS 

Then, again, when he has finished the exercise 
he should be given a chance to revise it. Many of 
the mistakes which we point out to him he could 
quite well with a little trouble find out for himself. 
When you or I write anything, rarely do we leave 
it as it first flowed from the pen. We set it aside 
and read it again later ; we score out superfluous 
words, change awkward phrases, rearrange the 
ideas, and sometimes, indeed, write the whole 
thing over and over again. All careful writers do 
this. If they do not actually do it on paper, they 
do it in their heads before committing it to paper. 
To revise and to remodel, to reflect upon what is 
written, and to reject even the good in favour of 
the better — that is at least part of the secret of 
clear and vigorous prose. We do this ourselves, 
but do not allow our pupils to do it. Often do we 
expect them to write without preparation ; always 
do we expect them to write without revision. 
Second thoughts are discouraged ; for erasures are 
discouraged. The pupil must try to present a 
fair page of writing without blot or blemish. So 
chary are the children of crossing anything out 
that if they make a mistake in phraseology or in 
spelling, they enclose the peccant word in brackets 
and leave it there. Let the teacher countenance, 
nay praise, the untidy page (provided the untidi- 
ness is due to careful thinking, not to careless writ- 
ing), and he will find his pupils falling into a habit of 
self-criticism. If the writing has become illegible 
the piece should, of course, be re-written. The 
stages of a composition exercise are, therefore, 
three : preparation, rough draft and final copy. 
And they may require three distinct lessons, or 



COMPOSITION 213 

any two sequent stages may occupy one lesson, or 
any one stage may spread over many lessons. 

So much for correcting. The marking proper, 
the measuring of the achievement, still remains to 
be done. And in that lies the crux of the difficulty. 
So complex is the thing to be measured, so numerous 
the criteria of merit, so diverse the points of view, 
that it is almost impossible to find different ex- 
aminers of the same scripts arriving at the same 
marks. They form different estimates because they 
attach different values to the component factors. 
Some think highly of quantity, others of quality ; 
some of ideas, others of style ; some of wealth of 
words, others of clearness of diction ; some of 
logical arrangement, others of sound and rhythm. 
Indeed, there is no end to the qualities which may 
be exalted by some and belittled by others. In 
measuring the achievement we are measuring a 
medley. It is as though we were trying to repre- 
sent the value of a room by a number which should 
sum up the size of the room, its shape, the lighting, 
the ventilation, the convenience of the fittings, 
the pattern of the wall-paper, the state of the floor, 
and a host of other qualities and quantities. The 
consequence is that in appraising a piece of writing 
we rely on the general impression left on our minds 
after reading it. In fine, we do not measure at 
all : we guess. True, it is not a pure guess : but 
neither is it a pure guess when we guess the height 
of a building by looking at it. We have data to go 
upon, but our mode of estimating is purely sub- 
jective. The standard by which we judge is our 
own standard and nobody else's. And the aim of 
the modern movement of reform in testing is to 



2i 4 MENTAL TESTS 

provide objective standards — standards that are 
everybody's standards. 

In America they try to objectify the standard in 
composition by means of a scale of specimens. 
Certain pieces are standardised by a number of 
reputable examiners ; they are arranged in order 
of merit, and assigned definite marks. This is 
then used as a scale by reference to which com- 
position exercises are measured. Five such scales 
are in general use, of which the Hillegas-Thorndike 
is apparently the most popular. This scale has 
15 grades of merit, ranging in marks from o to 95 — 
presumably out of a maximum of 100. The sixth 
specimen from the bottom reads as follows — 

" De Quincy. 

" First : De Quincy's mother was a beautiful 
women and through her De Quincy inhereted 
much of his genius. 

" His running away from school enfluenced him 
much as he roamed through the woods, valleys and 
his mind became very meditative. 

" The greatest enfluence of De Quincy's life was the 
opium habit. If it was not for this habit it is doubt- 
ful whether we would now be reading his writings. 

" His companions during his college course and 
even before that time were great enfluences. The 
surroundings of De Quincy were enfluences. Not 
only De Quincy's habit of opium but other habits 
which were peculiar to his life. 

" His marriage to the woman which he did not 
especially care for. 

" The many well educated and noteworthy 
friends of De Quincy," 



COMPOSITION 215 

This specimen is labelled Quality 47. What are 
we to think of it ? It reads as though the writer 
had been put to read something about De Quincey, 
had ill-digested it, and had tried to reproduce it ; 
not because he wanted to but because he had to. 
It may be typically American ; it certainly is not 
typically English. As it stands half-way up the 
scale we are, I presume, to regard it a"s an average 
performance. But the average performance in our 
English schools bears so slight a resemblance to 
this specimen that the two are in no way com- 
parable. The bulk of the children's writings strike 
a more even and a more genuine note. We never 
find a pupil using such booky words and showing 
at the same time so feeble a grasp of the structure 
of the sentence. If he can use the colon (he rarely 
can, by the way) he will not bungle at the apos- 
trophe. If he uses long words he generally knows 
how to spell them. Indeed, it would be difficult 
to pick up in our schools a piece of composition 
which, exhibiting the same combination of merits 
and defects, could be confidently judged as equal 
to the standard sample, and therefore deserving 
of forty-seven marks out of a hundred. 

There is the further difficulty of comparing dis- 
parate types of composition. To equate an essay 
with a story is by no means easy. A realisation of 
this difficulty led to the formulation of the Harvard- 
Newton scale, which comprises four distinct series 
of samples, one for each of the four common forms 
of discourse : narration, description, argumentation 
and exposition. But the whole question of the 
value of a scale of samples is still open. It is certain 
that its worth has never been clearly demonstrated, 



2i 6 MENTAL TESTS 

In one group of investigations upon one particular 
scale, indeed, it was actually found that teachers 
who used a scale of this kind showed greater vari- 
ability in their marking than those who adopted the 
usual plan of relying on general impression. In 
fact, they measured better without the scale than 
with it. On the other hand, it is claimed that 
with practice this variability decreases, so that after 
a time the advantage in steadiness will lie on the 
side of the scale. Be that as it may, its merits 
are not so obvious as to lead to its adoption in 
other countries. If it ever comes to England it must 
put on English garb. The sample pieces must be 
taken from English schools and standardised afresh. 

A promising line of inquiry has been opened up 
by Dr. Kimmins in his inquiry into the methods 
of expression used by London children in essay 
writing at different ages. (The Journal of Experi- 
mental Pedagogy, III, 289.) The criterion used 
by Dr. Kimmins is the type of sentence employed. 
From this point of view the most significant change 
with increasing age seems to be the less frequent 
use of the simple unrelated sentence, and the more 
frequent use of the complex sentence. But im- 
portant as is this way of looking at children's writ- 
ings, it is not the only way : it merely marks one 
point of merit out of many. 

There is, in fact, no help for it : we must, for 
the present at least, fall back upon the method of 
personal impression. And, indeed, when we re- 
member that in addition to the more tangible 
features of a piece of writing, there is always that 
peculiar appeal to our aesthetic sense which defies 
$11 measurements and all standards — when, in fact, 



COMPOSITION 217 

we remember that it is an artistic product as well 
as an intellectual product — we find it hard to see 
how the subjective standpoint can ever be out- 
grown. There are, however, certain definite things 
we can do to bring our individual judgments into 
closer unison. 

First, we must realise the roughness of the scale 
we are capable of using, and give up trying to 
calibrate more finely than the conditions warrant. 
To pretend to find 100 degrees of difference in 
however huge a number of papers, is to expose 
oneself to ridicule. Who can say, with any measure 
of confidence, that one paper merits 58 marks 
exactly and another 59 ? — unless, indeed, he works 
on some mechanical system of adding sentences, 
of deducting for errors, and of ignoring all the 
broader and more spiritual issues. The most finely 
graded scale in America, the Hillegas-Thorndike, 
has only 15 degrees of merit ; the others have 
respectively 10, 9, 8 and 6. At our universities it 
has ever been the custom to grade essays in four 
groups, assigning to each one of the first four 
letters of the Greek alphabet, with an occasional 
plus or minus to indicate finer shades ; and even 
this broad classification inspires in the under- 
graduate no great degree of confidence, main- 
taining, as he often does, that — 

" 'Twixt right and wrong the difference is dim, 
'Tis settled by the moderator's whim ; 
Perchance the delta on your paper marked 
Means that his lunch has disagreed with him." 

Having fixed upon the number of grades of merit 
(five is probably enough tQ stajt with) we must 



2i 8 MENTAL TESTS 

criticise the efficiency of our marking by observing 
the way in which our scores are distributed. If, 
for instance, we use five grades the coefficients in 
the expansion of (x + i) 4 , that is, i, 4, 6, 4 and 1 
give the probable or normal distribution. Generally 
speaking, out of every 16 papers 1 should receive 
one mark, 4 two, 6 three, 4 four and 1 five. If ten 
grades are used, the expansion of (1 + x) 9 , that is, 
1, 9, 36, 84, 126, 126, 84, 36, 9 and 1, apportions 
the number of papers that should, in a reasonable 
system of marking, receive the scores from 1 to 10 
consecutively. This, however, is a guiding principle, 
not a compelling principle. It helps the teacher in 
cases of doubt, it shows up the defects of a faulty 
system, but it cannot decide what marks are actually 
merited. The real starting-point is neither the best 
paper nor the worst, but the middle or average. 
The marks should crowd round this middle, but at 
each end there should be elbow-room. This aver- 
age is the standard which the marker should have 
fixed in his mind, and with which he should mentally 
compare the individual papers. There must be 
much provisional marking before this standard is 
fairly established. And in the case of the class 
teacher it is a standard which should be constantly 
rising, and should be assigned a constantly increasing 
value. 

Having developed for himself a sensible system 
of marking, the teacher should now impart it to his 
pupils. He should teach them how to mark. It 
will save him hours of useless toil, will alter the 
pupils' attitude towards his judgments, and will 
evoke in them a healthy spirit of self-criticism. 
At present the schoolboy never thinks of challenging 



COMPOSITION 219 

the teacher's verdict. He regards it not as a 
valuation but as a gift. He asks himself, " What 
mark has he given me ? " He should learn to ask, 
" What mark have I earned ? " And he should be 
able to say approximately whether his wage is 
correct, and have the right to challenge the figure. 
One of the pupils should occasionally read his 
composition to the class, and the rest be required 
to record individually and independently their 
estimate of its merit. After a little practice it is 
surprising how close together the estimates become. 
The scholars tend more and more to agree with 
one another and to agree with the teacher ; and 
soon the marking of a complete set of papers may 
safely be delegated to one of the scholars. He may 
be trusted to take pains over the task, knowing as 
he does that his marks will be carefully scrutinised 
by the writers, that his corrections and his findings 
will in some cases at least be challenged, and that 
he is to-day judging the work of one who to-morrow 
may become his judge. When the marked papers 
are distributed there will probably be much com- 
motion in the class. There will be a simmering of 
indignation and protest. And if the teacher has 
" nerves " he had better not try the system. With 
patience and tact, however, all the troubles will 
disappear. The teacher becomes the umpire be- 
tween the plaintiff, who states his grievance, and 
the marker, who has to defend both his corrections 
and his assessment. And the discussion that arises 
will be of more value to both pupils than much 
red ink and much blue pencil. In course of time 
the class will become educated to this sort of thing, 
and the members will take kindly and calmly the 



220 MENTAL TESTS 

criticisms of their fellows. It affords the same sort 
of moral training as boxing : it teaches them to 
take hard knocks without losing their tempers. 
Moreover, they are really learning to write English. 
No claim of novelty or of originality is made for 
this system. In modified form it has been used 
by others, and used with signal success. Nor must 
the teacher think that it entirely relieves him of 
the burden of marking : it only reduces the burden. 
In all cases he is the final arbiter : in important 
examinations he is the sole arbiter. And when he 
does mark he should mark very carefully; for his 
papers will now go back to trained critics. 



APPENDIX 



SOCRATES ON INTELLIGENCE 



There is little doubt that the dream itself was 
due to the lunch ; but the content of the dream 
was determined by other things. It was holiday 
time. In the morning I had taken a long and 
solitary walk ; and, pondering over the question 
of the discipline of the mind, had followed trains 
of thought which led to flatly contradictory issues. 
After a somewhat hearty lunch I retired to my 
study and took down from the shelves a volume 
of Jowett's translation of Plato. The book rested 
on the broad arm of my reading-chair, and as I 
turned over the leaves I was overcome with drowsi- 
ness and fell into a profound sleep. And as I slept 
I dreamed a dream. And I thought I stood in 
the streets of a strange city, which by some obscure 
process of reasoning or intuition I knew to be the 
ancient city of Athens. And of those who passed 
along the sunlit street two men specially arrested 
my attention. One of them was short and un- 
gainly, with a snub nose and protuberant eyeballs. 
His feet were bare and his simple cloak old and 
weather-stained. Indeed, his unattractive aspect 
formed a marked contrast with that of his com- 
panion, who, although a somewhat older man, 
suggested by his dress and general bearing the 



222 APPENDIX 



old Greek ideal of a gentleman — xaloxayaBoq. 
Yet was the ill-favoured one not devoid of a certain 
native dignity ; and I had no difficulty in recognising 
him as Socrates. Who the other was I could merely 
surmise. I followed them for some distance until 
they turned into a porch and knocked at a door 
of finely chased bronze. Presently the door was 
opened by a slave, and passing along a narrow hall 
we abruptly entered a room equipped with book- 
shelves, a pedestal desk and oak furniture of modern 
design. A severe-looking person in spectacles who 
was sitting at the desk rose to greet his visitors and 
bade them be seated. 

The anachronisms of the dream are glaring and 
palpable ; but during the dream itself they not 
only failed to astonish me : they entirely escaped 
my notice. It seemed quite right and fitting that 
Socrates should be conversing in English with a 
black-coated gentleman who quoted Tennyson. 
There appeared no historical inconsistency in the 
reference to prospectuses, school examinations and 
medical inspection. Nor did the fact in the least 
surprise me, that although I was present the whole 
time nobody seemed to take the slightest notice 
of me. Of the conversation that took place in that 
strange-familiar room my recollection is clear and 
vivid, and a faithful record thereof is herewith 
given — 

Soc. Hearing of your fame as a schoolmaster, 
Sophisticus, I have come to consult you about 
my two sons, one of whom is nine and the 
other ten years of age. I have brought with 
me my old friend Crito, who also takes much 



APPENDIX 223 



interest in the lads. We wish to know how 
best they may be trained in wisdom and virtue. 

Soph. Well, Socrates, I do not think you could do 
better than send them to my school. 

Soc. Many of my friends say the same thing ; and 
that, indeed, is why I came to you. You will, 
I am sure, put it down to pardonable anxiety 
on the part of a father if I seek, by asking you 
questions, to assure myself that my sons will 
get at your school a sound education. 

Soph. You may ask me as many questions as you 
like, Socrates, and I will do my best to answer 
you. 

Soc. Tell me, then, Sophisticus, what will my boys 
learn in your school ? 

Soph. They will learn everything that an educated 
man should know. There is my prospectus. 
You will see therein the full list of subjects. 

Soc. But I see nothing here about the teaching of 
virtue. Is not that one of the subjects ? 

Soph. We do not put that down, Socrates ; but 
we do teach our pupils to be good. We explain 
to them the sacred writings, and we look very 
carefully after their morals. 

Soc. And I see nothing here about wisdom. You 
will admit that a boy may know a large number 
of things and yet not be truly wise. 

Soph. I readily admit that. Although it is not 
put down in my prospectus, that is really the 
supreme aim and purpose of my school. We 
have discarded the old-fashioned word " wis- 
dom," and use the word "intelligence" in- 
stead ; but it means the same thing. My boys 
get a good training ; their intelligence is 



224 APPENDIX 



awakened. That is in fact the chief way in 
which my school differs from most other 
schools. It is not a place where " knowledge 
comes but wisdom lingers." Our aim is not 
merely to prepare boys for examinations ; 
what we really pride ourselves on doing is in 
producing general intelligence. 

Soc. I begin to understand. But it is a pity you 
do not put this down in your prospectus, 
Sophisticus, for I have for years been looking 
for a school where they train intelligence, as 
you call it, and have never found one. I see, 
however, that you advertise the fact that pupils 
are prepared for certain examinations. 

Sopb. If I did not put that down, Socrates, I fear 
I should get no pupils at all. But what I really 
try to cultivate is general intelligence. 

Crito. Don't you see, Socrates, that that is the 
explanation he reserves for the parents of 
children who fail at the examinations. 

Soc. That suspicion, Crito, is unworthy of you, 
and does injustice to a great schoolmaster like 
Sophisticus. I indeed prefer to believe that 
he seeks to produce general intelligence, and 
that success at examinations is a sort of by- 
product. 

Sopb. You state the case truly, Socrates. 

Soc. But tell me what you mean by giving the boys 
a good training. 

Sopb. I mean that we cultivate their mental 
powers. We teach them not only to know, 
but to do. We make them remember better, 
observe better, and reason better, and, to put 
it generally, we make them better thinkers. 



APPENDIX 225 



Soc. That, indeed, is a great achievement. But 
you must not bewilder me by telling me so 
much at once, for I have a bad memory, and 
can only deal with one thing at a time. Tell 
me how you make a boy more observant. 

Soph. By giving him practice in observation, of 
course. 

Soc. By practice, you mean that he repeats the 
same act over and over again ? 

Soph. Just so. 

Soc. And he does it better the second time than 
the first ? 

Soph. Yes. 

Soc. And the third time better than the second ? 

Soph. Precisely. 

Soc. But is not this what we call forming a habit ? 

Soph. I suppose it is. 

Soc. Observation, then, is a habit ? 

Soph. I have never thought of it in that light, 
Socrates, but I think you are right. 

Soc. I do not say that I am right : I am trying to 
find out what you can tell me about the matter. 
You do not mind my putting these questions ? 

Soph. Of course not, Socrates. I have heard of 
your custom of questioning people, and I am 
glad to have an opportunity of hearing you. 

Soc. Tell me, then, does training consist in any- 
thing else but the formation of habits ? 

Soph. It depends on what you mean by habits. 

Soc. Does not an act tend to become easier by 
repetition ? 

Soph. Yes. 

Soc. And it is true of an act of thought, of feeling, 
or of will, as well as of a physical act ? 
Q 



226 APPENDIX 



Soph. Certainly. 

Soc. Shall we agree to call any act that has been 
improved by practice a habit ? 

Soph. It seems to be a suitable name for it. 

Soc. Then training consists in forming habits ? 

Soph. Yes. 

Soc. And nothing else ? 

Soph. And nothing else. 

Soc. And is intelligence a habit ? 

Soph. Well, I should not be disposed to call in- 
telligence a habit. It seems to me to be less 
a habit than observation even. 

Soc. And yet you said that you could train in- 
telligence. 

Soph. There does seem to be a contradiction some- 
where. And yet I am sure I can train intelligence. 

Soc. Let us try again. What is intelligence ? 

Soph. Now you have asked me a very difficult 
question. I can pick you out my most in- 
telligent pupils, but I cannot tell you off-hand 
precisely in what this intelligence consists. 

Soc. Are they necessarily intelligent if they can 
read well ? 

Soph. No. 

Soc. Or write, or draw, or sing well ? 

Soph. No. 

Soc . Or repeat poetry, or remember history ? 

Soph. No. 

Soc. Or do arithmetic ? 

Soph. It depends upon the kind of arithmetic. 

Soc. What kind of arithmetic can an unintelligent 
boy do ? 

Soph. Simple straightforward sums, such as the 
common rules which he has been taught. 



APPENDIX 227 



Soc. And what kind can an intelligent boy alone do ? 

Soph. Problems. 

Soc. And what is the essential difference between 
the two ? 

Soph. The unintelligent boy can do sums which 
he has previously practised, or has at least 
been shown how to do. The intelligent boy 
can do sums which are not quite the same as 
any others which he has done or been shown 
how to do. 

Soc. And is intelligence shown in any other subject 
besides arithmetic ? 

Soph. Certainly, a boy may show intelligence in 
geography, or history, or science, or hand- 
work, or indeed in any subject which is not 
purely mechanical. 

Soc. And is it the novel part that requires intelli- 
gence in other subjects as in arithmetic ? 

Soph. That is right, Socrates, you have made it 
quite clear. It is the new, the unfamiliar part 
of any given situation that calls for intelligence 
on the part of a boy. 

Soc. I am glad to hear you say that, Sophisticus, 
for that simplifies the case. Tell me, does 
training have to do with the familiar, or with 
the unfamiliar ? With the old or with the new ? 

Soph. I do not see what you mean. 

Soc. Does not training involve doing the same 
thing over again ? 

Soph. Yes, we agreed that it was based on practice. 

Soc. And when you are trained to deal with any 
kind of situation that situation is no longer 
new ? it is no longer unfamiliar ? 

Soph. Quite so. 

Q2 



228 APPENDIX 



Soc. Then a trained faculty has to do with familiar 

material ? 
Soph. Yes. 

Soc. And intelligence deals with the unfamiliar ? 
Soph. Yes. 

Soc. Then intelligence cannot be trained ? 
Soph. No, Socrates, I will never admit that. 

There must be some flaw in the argument. 

I think I see what it is. The situation which 

you call new or unfamiliar is never wholly new. 

There is always much that is old, and rarely 

more than a little that is new. 
Soc. But the unintelligent pupil can deal with the 

old part of the situation if he has been trained 

to it ? 
Soph. Yes. 

Soc. And if the new part is not dealt with, intelli- 
gence is not shown ? 
Soph. Quite so. 
Soc. Then it is only intelligence that can deal with 

the new part ? 
Soph. 



Soc. And no training can enable us to deal with 
the new ? 

Soph. It seems so. 

Soc. Then we are again back in the same position. 
Intelligence cannot be trained. 

Soph. Although I cannot refute your argument, 
Socrates, in your own way, I can do it in 
another way. If you will send your boys to 
me you will find that at the end of a year 
they will be much more intelligent than when 
they came ; and I call that a much stronger 
argument than even you can devise. 



APPENDIX 229 



Soc. If you can do that I will believe that our 
discussion has somehow strayed from the 
truth. I will think over what you say. Come, 
Crito, let us depart, for I see that Sophisticus 
is impatient of all this talk about things which 
he can do but cannot explain. 
(After the usual greetings they take their leave.) 

Crito. Tell me, Socrates, do you really think that 
intelligence cannot be cultivated ? 

Soc. I should be glad to be convinced to the con- 
trary. I fear there were many errors in our 
discussion with Sophisticus, but not of the 
nature that you imagine. You noticed that 
we seemed to agree to call observation a 
habit ? 

Crito. I noticed that, Socrates. 

Soc. And do you think it is a habit ? 

Crito. I thought so at the time, but I don't feel so 
sure about it now. 

Soc. Tell me, Crito, is breathing a habit ? 

Crito. We never call it a habit. 

Soc. But is it not an act which we are continually 
repeating ? 

Crito. Certainly. 

Soc. How, then, does it differ from an act which 
everybody calls a habit, such as the trick which 
some people have of frequently stroking the 
beard ? 

Crito. Only some people stroke their beards, but 
everybody breathes. 

Soc. And why does everybody breathe ? 

Crito. He cannot help it, Socrates. It is a natural 
power which he brings with him when he comes 
into the world. 



230 APPENDIX 



Soc. And why does not everybody who has a beard 

stroke it ? 
Crito. Because it is a habit which some acquire, 

and some do not. 
Soc. A habit, then, is a personal acquisition ? 
Crito. Yes. 
Soc. And in that sense breathing is not a habit, 

but a natural power ? 
Crito. Yes. 
Soc. Can a natural power be improved, do you 

think ? 
Crito. I think it can, Socrates. My grandchildren 

who are now at school have breathing exercises 

every day. And the physician visits the school, 

and examines the children's noses and air 

passages, so that obstructions may be removed. 

People, too, who have their voices trained say 

that attention is paid not to their throats 

where the sound is produced, but to the 

mechanism for breathing. They are in fact 

taught to breathe better. 
Soc. Tell me any way in which children at school 

are taught to breathe better. 
Crito. They are taught to use handkerchiefs, and 

to breathe through the nose, and to breathe 

deeply. 
Soc. And is not the proper use of a handkerchief a 

habit ? 
Crito. Certainly. 
Soc. And breathing through the nose, rather than 

the mouth, is that a habit, too ? * 

Crito. It is a habit. 
Soc. And what shall we say for breathing deeply ? 

cannot that become a habit ? 



APPENDIX 231 



Crito. It can. 

Soc. Then, shall we be right in saying that a 
natural power like breathing can be improved 
by forming certain habits which render that 
power more effective ? 

Crito. We shall be right in saying that. 

Soc. And is not the same thing true of observation, 
which we have agreed to regard as a natural 
power ? 

Crito. Yes. 

Soc. And is not intelligence a natural power inas- 
much as everybody possesses it in some degree ? 

Crito. Yes. 

Soc. Then intelligence can be improved in the 
same way as breathing and observation can be 
improved ? 

Crito. It seems so. 

Soc. Then Sophisticus is right after all, and in- 
telligence can be trained. 

Crito. And yet, Socrates, it seemed to me while 
you were arguing with Sophisticus that the 
opposite was true. 

Soc. May not both conclusions be true ? 

Crito. How is that possible, Socrates ? 

Soc. I fear, Crito, that we have been confusing 
ourselves and obscuring the argument by using 
the same words in different senses. When we 
talked about observation we at one time 
assumed it to be a simple power which could 
either be trained or not be trained ; at another 
time we spoke of it as though it were a group 
of distinct and separate powers, some, if not 
all, of which could be trained. And in the 
same way we have been deceived by different 



232 APPENDIX 



meanings of the word intelligence. I think, 
Crito, that you and I had better go to school 
again to learn the right use of words. 
Crito. I am quite willing to go with you, Socrates, 
provided you can find somebody to teach us. 

Meanwhile we were walking along narrow streets 
whose bare and windowless walls were relieved here 
and there by doors that opened outwards into the 
street. One of these doors, more pretentious than 
the rest, was protected by a porch, near the entrance 
of which stood one of those images of Hermes which 
Alcibiades was supposed to have mutilated. As we 
passed this porch, which we did just as Crito had 
finished speaking, I touched the image with my 
hand and it fell to the ground with a loud crash. 
So loud indeed was it that I woke up with a start, 
and looking down I saw the volume of Jowett's 
Plato lying flat upon the floor. 



INDEX 



Absurdity tests, 30, 38, 39, 76, 

154 

Adams, J., 109 

Addition, 161 ff. 

jEsthesiometer, 9-10 

Age-performance, 13-14 

Age test, 60 

Alcibiades, 232 

American tests, 15, 20, 29, 40, 

46, 145, 214, 215 
Analogies test, 32, 33 
Applied arithmetic, 191 ff. 
Arithmetic, 19, 112, 160 ff., 226 
Arithmetical devices, 190 
Association test, 37, 80 
Average, 123 ff. 
Ayres, L. P., 112, 156-7 

Bagley, W. C, 200 

Bareme d' instruction, 40, 107, 

"I, 134 
Bayes, W., 203 
Bickersteth, M. E., 198-9, 200, 

202 
Binet, Alfred, 11, 13 ff., 17, 20, 

23. 27, 30, 35 ff., 48 ff., 107, 

in, 197 
Blackboarditis, 182-3 
Bottle test, 34 
Breathing, 229-30 
British Association, 47, 160 
Brown, W., 47 
Browning, R., 153 
Burt, Cyril, viii, 11-12, 16, 18, 

27, 45, 47, 48 ff., 90 ff., 115, 

127, 157-8, 161, 200 

Cancellation, 34 

Carey, N., 47, 200 
Central tendency, 122 ff. 
Coin tests, 63, 68, 72, 73 



Colour test, 61 

Columbia University, 15, 42 

Complexes, v 

Complimentary addition, 173-4 

Composition, 19, 45, 87, 128-9, 

210 ff. 
Correlation, 17, 18, 25, 26 
Counting test, 55, 62, 71 
Courtis, S. A., 112, 160 
Criminology, 5 
Crito, 222 ff . 
Cube test, 204-5 

Dale system of reading, 141 ff. 
Darwin, C, 5 
Date test, 72 
Day of week test, 63 
Decomposition method of sub- 
traction, 168 ff. 
Definitions test, 64, 73, 84 
De Quincey, 215 
Dictation, 158-9 
Dictation test, 69 
Differences test, 68, 86, 88 
Digits test, 36, 50, 55, 61, 73, 80 
Distribution, 115 ff. 
Dotting machine, 11, 46 
Drawing, 132 

Drawing tests, 13, 62, 75, 85, 86 
Dynamometer, 7 

Einstein, 2 

English, H. B., 47 

Equal addition method of sub- 
traction, 168 ff. 

Ergograph, 7 

Error, Curve of, 120 

Evans, Miss Lloyd, 153 

Examinations, 2, 14, 18, 19, 27, 
29, 41 ff., no, 121 ff., 127, 
131 



233 



234 



INDEX 



Finger test, 62 
French test, 33 
Frequency-column-graph, 117 

Gall, F. J., 3, 4 
Galton, F., 6, 10, 17 
Gilbreth, F. B. and L. M., 207-8 
Goddard's revision of Binet's 

tests, 15 
Gray, P. L., 160 
Green, J. A., 47, 160 

Hart, Bernard, 47 
Harvard-Newton scale, 215 
Hawkins, H. W., 202 
Heights of Englishmen, 115 ff. 
Heine, H., 5 
Hillegas-Thorndike scale, 214 

Images, 10 

Indirect measurement, 3 ff., 26 
Individual work, 142 ff., 178 ff. 
Instructions tests, 40, 50, 59 
Intelligence, 6,11 ff., 21 ff., 29 ff ., 

48 ff., 221 ff. 
Intelligence quotient, 49 
Interquartile range, 125 ff. 

James, Wm., 27, 36 
Jevons, S., 1 
Jones, Emrys, vii 
Judd, C. H., 112 

Kansas silent reading tests, 

146-7 
Kelly, T. L., 205 
Kimmins, C. W., 216 
King John, Ballad of, 30-31 
Knowledge, 22 ff ., 106 ff . 

Lamb, C., 4, 210 
Lancashire, Reading in, 140 
Lavater, J. K., 4 
Lewis, E. O., 47 
Lines tests, 56, 82 
Lombroso, C., 5 

Manual ability, 45, 196 ff. 
Mathematics, i, 17, 130 
McDougall, W., 10, 11, 47, 198 
Mclntyre, J. L., 47 
Mean deviation, 125 ff. 



Measurements, v, vi, 2, 3 

Median, 123 ff. 

Memory, 10, 36-7, 176 ff. 

Milton, J., 4 

Months test, 73 

Moore, R. C, 200 

Morning and afternoon test 

60 
Motion study, 208 
Motor ability, 196 ff. 
Munroe, W. S., 112 
Myers, C. S., 47, 208 

Name test, 51 

Newton, I., 1 

Normal distribution, 17, 118 ff. 

Norms, 21, 108 ff., 139, 153, 160. 

165, 166, 188, 191, 195 
Nunn, T. P., viii, 115 

Objects tests, 52, 68 
Oblong test, 64 
Observation, 225 ff. 
CEdipus, 3, 31, 33 
Ogive, 116 
Oral arithmetic, 186 ff. 

Pearson, K., 6, 18 

Perseus, 31 

Phrenology, 3-4 

Physiognomy, 4-5 

Pictures tests, 52, 56, 57, 66, 67, 

82 
Plato, 221, 232 
Plunger apparatus, 198 ff. 
Porteus, S. D., 206 
Porteus test, 206-7 
Poverty and attainments, 139- 

40, 189-90 
Practical ability, 196 ff. 
Practice in arithmetic, 1 79 
Probable error, 126 
Probability curve, 119 
Problems test, 83 # 

Quetelet, L. A. J., 17 
Quartile, 125 ff . 

Reaction-time, 7, 8 

Reading, 70, 73, no, in, 134 ff. 

Reading-books, 143 
Reasoning tests, 16, 90 ff. 






INDEX 



235 



Recommendations for improving 

arithmetic, 185-6 
Repetition test, 54, 60, 66, 69, 84 
Rhyme test, 81 
Riddles, 3, 29, 31. 33 
Right and left test, 66 
Rivers, W. H. R., 10 

Samson, 3 

S avoir j aire tests, 70-1, 78 

Scale of samples, 20-1 

Scholarships, 44 

Schuster, E., 47 

Sensory discrimination, 9-10 

Sentence tests, 74, 81 

Sex differences, 140 

Sex -naming test, 51 

Shakespeare, W., 210 

Simon, Th., 48 

Skew curve, 122 

Smith, M., 47 

Socrates, 221 ff. 

Spearman, C, 18, 24, 25, 27 

Spelling, 112, 155 ff. 

Sphinx, 3, 31, 33 



Spurzheim, J. G., 3, 4 
Standard deviation, 126 ff . 
Standardisation, 19, 34 ff ., 106 ff . 
Stanford Revision of Binet's 

tests, 15 
Stern, W., 49 
Subtraction, 162-3, ID 8 ff-. 187 

Tables in arithmetic, 174 ff. 

Tapping, 7, 197 ff. 

Taylor, N., 47 

Tennyson, A., 222 

Terman, L. M., 15, 17, 49, 112 

Thorndike, E. L., 2, 20, 24, 27, 

112 
Tossing coins, 119 
Transcription test, 63 

Vocational tests, 8 

Weber-Fechner law, 8-9 

Weights tests, 61, 73 

Winch, W. H., 13, 18, 47, 176 

Yerkes' point-scale, 15 



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